Pub Date : 2023-11-15DOI: 10.1080/00036811.2023.2283136
Yu Liu, Xingxing Liu
In this paper, we investigate the nonexistence of the periodic peakon and peakon for a highly nonlinear shallow-water model, which has been recently derived from the full governing equations for tw...
本文研究了一个高度非线性浅水模型的周期峰子和峰子的不存在性，该模型是最近由两个完全控制方程导出的。
{"title":"Nonexistence of periodic peakon and peakon for a highly nonlinear shallow-water model","authors":"Yu Liu, Xingxing Liu","doi":"10.1080/00036811.2023.2283136","DOIUrl":"https://doi.org/10.1080/00036811.2023.2283136","url":null,"abstract":"In this paper, we investigate the nonexistence of the periodic peakon and peakon for a highly nonlinear shallow-water model, which has been recently derived from the full governing equations for tw...","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"64 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138541015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-14DOI: 10.1080/00036811.2023.2281506
Jinliang Wang, Hao Qu, Desheng Ji
AbstractIn this paper, we consider a reaction–diffusion dengue model on a varying domain that monotonically increases in time and gradually approaches saturation arising from environmental change. By the upper and lower solutions, comparison principle, asymptotic autonomous semiflows and the technique of Lyapunov function, we investigate the stabilities of equilibria in terms of the basic reproduction number ℜ0ρ. The results show that (i) if ℜ0ρ>1, the nontrivial solutions starting from the upper and lower solutions of the model approach to the set formulated by the maximal and minimal solutions of its related elliptic problem; (ii) the disease-free equilibrium is globally asymptotically stable when ℜ0ρ<1. Comparing our problem in different settings including growing domain, fixed domain and without spatial structure, our results demonstrate that the disease can spread in the growing domain, while vanish in the fixed domain; and the spatial model decreases the transmission risk compared with the system without spatial structure.Keywords: Dengue modelgrowing domainbasic reproduction numbervanishing and spreadingLyapunov functionMathematic Subject classifications: 34K3035K5735Q8092D25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by National Natural Science Foundation of China (No. 12071115) and Heilongjiang Natural Science Funds for Distinguished Younger Scholar (No. JQ2023A005).
{"title":"Analysis of a reaction–diffusion dengue model with vector bias on a growing domain","authors":"Jinliang Wang, Hao Qu, Desheng Ji","doi":"10.1080/00036811.2023.2281506","DOIUrl":"https://doi.org/10.1080/00036811.2023.2281506","url":null,"abstract":"AbstractIn this paper, we consider a reaction–diffusion dengue model on a varying domain that monotonically increases in time and gradually approaches saturation arising from environmental change. By the upper and lower solutions, comparison principle, asymptotic autonomous semiflows and the technique of Lyapunov function, we investigate the stabilities of equilibria in terms of the basic reproduction number ℜ0ρ. The results show that (i) if ℜ0ρ>1, the nontrivial solutions starting from the upper and lower solutions of the model approach to the set formulated by the maximal and minimal solutions of its related elliptic problem; (ii) the disease-free equilibrium is globally asymptotically stable when ℜ0ρ<1. Comparing our problem in different settings including growing domain, fixed domain and without spatial structure, our results demonstrate that the disease can spread in the growing domain, while vanish in the fixed domain; and the spatial model decreases the transmission risk compared with the system without spatial structure.Keywords: Dengue modelgrowing domainbasic reproduction numbervanishing and spreadingLyapunov functionMathematic Subject classifications: 34K3035K5735Q8092D25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by National Natural Science Foundation of China (No. 12071115) and Heilongjiang Natural Science Funds for Distinguished Younger Scholar (No. JQ2023A005).","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"19 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134953570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-11DOI: 10.1080/00036811.2023.2282140
H. Khelifi
AbstractIn this paper, we investigate the existence and regularity of a capacity solution for a coupled nonlinear anisotropic parabolic-elliptic system, where the elliptic component of the parabolic equation involves thermal conductivities ai(u) that satisfy lims→+∞ai(s)=0 for all i=1,…,N. We work with anisotropic Sobolev spaces and use Schauder's fixed-point theorem to find weak solutions to approximate problems. In addition, we validate the convergence of a subsequence of approximate solutions to a capacity solution.Keywords: Capacity solutionsanisotropic parabolic-elliptic equationsweak solutionsthermistor problemfixed-point theoremregularityMATHEMATICS SUBJECT CLASSIFICATIONs: 35K6535M1035K6035J60 AcknowledgmentsThe author is grateful to the referees for their constructive comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"Anisotropic parabolic-elliptic systems with degenerate thermal conductivity","authors":"H. Khelifi","doi":"10.1080/00036811.2023.2282140","DOIUrl":"https://doi.org/10.1080/00036811.2023.2282140","url":null,"abstract":"AbstractIn this paper, we investigate the existence and regularity of a capacity solution for a coupled nonlinear anisotropic parabolic-elliptic system, where the elliptic component of the parabolic equation involves thermal conductivities ai(u) that satisfy lims→+∞ai(s)=0 for all i=1,…,N. We work with anisotropic Sobolev spaces and use Schauder's fixed-point theorem to find weak solutions to approximate problems. In addition, we validate the convergence of a subsequence of approximate solutions to a capacity solution.Keywords: Capacity solutionsanisotropic parabolic-elliptic equationsweak solutionsthermistor problemfixed-point theoremregularityMATHEMATICS SUBJECT CLASSIFICATIONs: 35K6535M1035K6035J60 AcknowledgmentsThe author is grateful to the referees for their constructive comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"9 24","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1080/00036811.2023.2279951
Govanni Granados, Isaac Harris
AbstractIn this paper, we consider inverse shape problems coming from diffuse optical tomography and the Helmholtz equation. In both problems, our goal is to reconstruct small volume interior regions from measured data on the exterior surface of an object. In order to achieve this, we will derive an asymptotic expansion of the reciprocity gap functional associated with each problem. The reciprocity gap functional takes in the measured Cauchy data on the exterior surface of the object. In diffuse optical tomography, we prove that a MUSIC-type algorithm that does not require evaluating the Green's function can be used to recover the unknown subregions. This gives an analytically rigorous and computationally simple method for recovering the small volume regions. For the problem coming from inverse scattering, we recover the subregions of interest via a direct sampling method. The direct sampling method presented here allows us to accurately recover the small volume region from one pair of Cauchy data, requiring less data than many direct sampling methods. We also prove that the direct sampling method is stable with respect to noisy data. Numerical examples will be presented for both cases in two dimensions where the measurement surface is the unit circle.Keywords: Diffuse optical tomographyhelmholtz equationMUSIC algorithmdirect samplingMathematics Subject Classifications: 35J0535J25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe research of G. Granados and I. Harris is partially supported by the NSF DMS Grant 2107891.
摘要本文考虑了由漫射光学层析成像和亥姆霍兹方程引起的逆形状问题。在这两个问题中，我们的目标是从物体外表面的测量数据重建小体积的内部区域。为了实现这一点，我们将推导出与每个问题相关的互易间隙函数的渐近展开式。互易间隙泛函接收物体外表面测量的柯西数据。在漫射光学层析成像中，我们证明了一种不需要评估格林函数的music型算法可以用于恢复未知的子区域。这为小体积区域的恢复提供了一种解析严密、计算简单的方法。对于来自逆散射的问题，我们采用直接采样的方法恢复感兴趣的子区域。本文提出的直接抽样方法使我们能够从一对柯西数据中准确地恢复小体积区域，比许多直接抽样方法需要更少的数据。我们还证明了直接抽样方法对于噪声数据是稳定的。在测量表面为单位圆的二维空间中，将给出这两种情况的数值例子。关键词:漫射光学层析成像;亥姆霍兹方程;music算法;直接采样;G. Granados和I. Harris的研究部分由NSF DMS Grant 2107891资助。
{"title":"Reciprocity gap functional for potentials/sources with small-volume support for two elliptic equations","authors":"Govanni Granados, Isaac Harris","doi":"10.1080/00036811.2023.2279951","DOIUrl":"https://doi.org/10.1080/00036811.2023.2279951","url":null,"abstract":"AbstractIn this paper, we consider inverse shape problems coming from diffuse optical tomography and the Helmholtz equation. In both problems, our goal is to reconstruct small volume interior regions from measured data on the exterior surface of an object. In order to achieve this, we will derive an asymptotic expansion of the reciprocity gap functional associated with each problem. The reciprocity gap functional takes in the measured Cauchy data on the exterior surface of the object. In diffuse optical tomography, we prove that a MUSIC-type algorithm that does not require evaluating the Green's function can be used to recover the unknown subregions. This gives an analytically rigorous and computationally simple method for recovering the small volume regions. For the problem coming from inverse scattering, we recover the subregions of interest via a direct sampling method. The direct sampling method presented here allows us to accurately recover the small volume region from one pair of Cauchy data, requiring less data than many direct sampling methods. We also prove that the direct sampling method is stable with respect to noisy data. Numerical examples will be presented for both cases in two dimensions where the measurement surface is the unit circle.Keywords: Diffuse optical tomographyhelmholtz equationMUSIC algorithmdirect samplingMathematics Subject Classifications: 35J0535J25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe research of G. Granados and I. Harris is partially supported by the NSF DMS Grant 2107891.","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"132 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135342379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1080/00036811.2023.2279955
Shiqi Zhang
AbstractIn this paper, we consider a singular Adams' inequality with logarithmic weights in the unit ball of R4. Our results extend the results of Zhu and Wang [Adams' inequality with logarithmic weights in R4. Proc Amer Math Soc. 2021;149(8):3463–3472] on Adams' inequality with logarithmic weights to singular case. Then, we study the existence of solutions for some weighted mean field equations, relying on variational methods and the singular Adams' inequality with logarithmic weights we previously established.Keywords: Singular Adams' inequalitylogarithmic weightsweighted mean field equations2010 Mathematics Subject Classifications: 35A2135A2335D3035J25 Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"A singular Adams' inequality with logarithmic weights and applications","authors":"Shiqi Zhang","doi":"10.1080/00036811.2023.2279955","DOIUrl":"https://doi.org/10.1080/00036811.2023.2279955","url":null,"abstract":"AbstractIn this paper, we consider a singular Adams' inequality with logarithmic weights in the unit ball of R4. Our results extend the results of Zhu and Wang [Adams' inequality with logarithmic weights in R4. Proc Amer Math Soc. 2021;149(8):3463–3472] on Adams' inequality with logarithmic weights to singular case. Then, we study the existence of solutions for some weighted mean field equations, relying on variational methods and the singular Adams' inequality with logarithmic weights we previously established.Keywords: Singular Adams' inequalitylogarithmic weightsweighted mean field equations2010 Mathematics Subject Classifications: 35A2135A2335D3035J25 Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"9 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135390126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-22DOI: 10.1080/00036811.2023.2271950
Laure Cardoulis, Michel Cristofol
AbstractIn this article we consider the inverse problem of simultaneously determining three coefficients of a FitzHugh–Nagumo type system defined in a bounded domain. We use a Carleman estimate to establish Hölder estimates for these coefficients by a finite number of measurements of only one component of the system.Keywords: Carleman estimatesinverse problemsstability resultPDE/ODE systemMathematic Subject classification: 35R30 Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"An inverse problem for a generalized FitzHugh–Nagumo type system","authors":"Laure Cardoulis, Michel Cristofol","doi":"10.1080/00036811.2023.2271950","DOIUrl":"https://doi.org/10.1080/00036811.2023.2271950","url":null,"abstract":"AbstractIn this article we consider the inverse problem of simultaneously determining three coefficients of a FitzHugh–Nagumo type system defined in a bounded domain. We use a Carleman estimate to establish Hölder estimates for these coefficients by a finite number of measurements of only one component of the system.Keywords: Carleman estimatesinverse problemsstability resultPDE/ODE systemMathematic Subject classification: 35R30 Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"27 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135461953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-21DOI: 10.1080/00036811.2023.2271941
Xin Zhong
AbstractWe establish the global existence and uniqueness of strong solutions for nonhomogeneous magnetic Bénard system with far field vacuum in the whole two-dimensional (2D) plane. In particular, the initial data can be arbitrarily large. Our method relies heavily on the structure of the system under consideration and spatial dimension.Keywords: Nonhomogeneous magnetic Bénard systemglobal well-posednessCauchy problemlarge initial datavacuum2020 Mathematics Subject Classifications: 35Q3576D0376W05 AcknowledgmentsThe author would like to thank the referees for their helpful suggestions and valuable comments, which helped him a lot to improve the presentation of the original manuscript.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research was partially supported by the National Natural Science Foundation of China [grant numbers 11901474 and 12371227] and the Innovation Support Program for Chongqing Overseas Returnees [grant number cx2020082].
{"title":"Global well-posedness for nonhomogeneous magnetic Bénard system","authors":"Xin Zhong","doi":"10.1080/00036811.2023.2271941","DOIUrl":"https://doi.org/10.1080/00036811.2023.2271941","url":null,"abstract":"AbstractWe establish the global existence and uniqueness of strong solutions for nonhomogeneous magnetic Bénard system with far field vacuum in the whole two-dimensional (2D) plane. In particular, the initial data can be arbitrarily large. Our method relies heavily on the structure of the system under consideration and spatial dimension.Keywords: Nonhomogeneous magnetic Bénard systemglobal well-posednessCauchy problemlarge initial datavacuum2020 Mathematics Subject Classifications: 35Q3576D0376W05 AcknowledgmentsThe author would like to thank the referees for their helpful suggestions and valuable comments, which helped him a lot to improve the presentation of the original manuscript.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research was partially supported by the National Natural Science Foundation of China [grant numbers 11901474 and 12371227] and the Innovation Support Program for Chongqing Overseas Returnees [grant number cx2020082].","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135511090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-21DOI: 10.1080/00036811.2023.2271946
Xinliang Li, Dandan Ding
AbstractWe first establish the existence of global strong solutions to the 3D inviscid incompressible magneto-micropolar equations with a velocity damping in Sobolev spaces HK(K⩾3), where the H3 norm of initial data is small, but its higher order derivatives could be large. Combining the H˙−s norm (0≤s<32) or B˙2,∞−s norm (0
{"title":"Global well-posedness and large-time behavior of solutions to the 3D inviscid magneto-micropolar equations with damping","authors":"Xinliang Li, Dandan Ding","doi":"10.1080/00036811.2023.2271946","DOIUrl":"https://doi.org/10.1080/00036811.2023.2271946","url":null,"abstract":"AbstractWe first establish the existence of global strong solutions to the 3D inviscid incompressible magneto-micropolar equations with a velocity damping in Sobolev spaces HK(K⩾3), where the H3 norm of initial data is small, but its higher order derivatives could be large. Combining the H˙−s norm (0≤s<32) or B˙2,∞−s norm (0<s≤32) of the initial magnetic field is finite with some tricky interpolation estimates, we show ‖∇nB(t)‖L2≤C0(1+t)−n2−32p+34 and two faster decay rates for the velocity and the micro-rotation field ‖∇n(U,w)(t)‖L2≤C0(1+t)−n2−32p+14, which are shown to be the usual Lp−L2 (1≤p≤2) type of the optimal time decay rates for 3D inviscid incompressible magneto-micropolar equations with damping. We then conclude the damping term contributes to weaken the assumption of initial condition and enhance the decay rate of velocity compared to the classical incompressible viscous magneto-micropolar equations. Meanwhile, for the 3D inviscid compressible magneto-micropolar fluid, the damping term also has the same effect on the decay rate of the velocity.Keywords: Global well-posednessoptimal decay ratesmagneto-micropolar fluidsvelocity dampingMathematics Subject Classifications (2010): 35Q3535B4076D03 AcknowledgmentsThe authors would like to thank the referees for their careful reading of the work and their many helpful suggestions. Thanks are also due to Professor Zhong Tan for his support and constant encouragement.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135511653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-21DOI: 10.1080/00036811.2023.2267576
Zai-Yun Peng, Zhi-Ying Peng, Gang Cai, Gao-Xi Li
AbstractIn this paper, an inertial subgradient extragradient algorithm is proposed to solve the pseudomonotone variational inequality problems in Banach space. This iterative scheme employs a new line-search rule. Strong convergence theorems for the proposed algorithms are established under the assumptions that the operators are non-Lipschitz continuous. Furthermore, several numerical experiments are given to show that our method has better convergence performance than the known ones in the literatures.COMMUNICATED BY: J. ZouKeywords: Variational inequalitiespseudomonotone operatorBanach spacesubgradient extragradient methodstrong convergenceMathematics Subject Classifications: 47H0547H0747H1054H25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe first author was supported by the National Natural Science Foundation of China (12271067), the Chongqing Natural Science Foundation (cstc2021jcyj-msxmX0080), the Group Building Project for Scientific Innovation for Universities in Chongqing (CXQT21021) and the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZD-K202200704). The second author was supported by the Chongqing Jiaotong University Postgraduate Research Innovation Project (2022S0070) and the Joint Training Base Construction Project for Graduate Students in Chongqing (JDLHPYJD2021016). The third author supported by the Chongqing Natural Science Foundation (CSTB2022NSCQ-MSX1318). The fourth author supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202000710), the Chongqing Natural Science Foundation (CSTB2022NSCQ-MSX1498).
{"title":"Inertial subgradient extragradient method for solving pseudomonotone variational inequality problems in Banach spaces","authors":"Zai-Yun Peng, Zhi-Ying Peng, Gang Cai, Gao-Xi Li","doi":"10.1080/00036811.2023.2267576","DOIUrl":"https://doi.org/10.1080/00036811.2023.2267576","url":null,"abstract":"AbstractIn this paper, an inertial subgradient extragradient algorithm is proposed to solve the pseudomonotone variational inequality problems in Banach space. This iterative scheme employs a new line-search rule. Strong convergence theorems for the proposed algorithms are established under the assumptions that the operators are non-Lipschitz continuous. Furthermore, several numerical experiments are given to show that our method has better convergence performance than the known ones in the literatures.COMMUNICATED BY: J. ZouKeywords: Variational inequalitiespseudomonotone operatorBanach spacesubgradient extragradient methodstrong convergenceMathematics Subject Classifications: 47H0547H0747H1054H25 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe first author was supported by the National Natural Science Foundation of China (12271067), the Chongqing Natural Science Foundation (cstc2021jcyj-msxmX0080), the Group Building Project for Scientific Innovation for Universities in Chongqing (CXQT21021) and the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZD-K202200704). The second author was supported by the Chongqing Jiaotong University Postgraduate Research Innovation Project (2022S0070) and the Joint Training Base Construction Project for Graduate Students in Chongqing (JDLHPYJD2021016). The third author supported by the Chongqing Natural Science Foundation (CSTB2022NSCQ-MSX1318). The fourth author supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202000710), the Chongqing Natural Science Foundation (CSTB2022NSCQ-MSX1498).","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"75 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.1080/00036811.2023.2271031
Yujie Li, Xiaoliang Cheng, Hailing Xuan
AbstractIn this paper, we are concerned with a class of second-order hemivariational inequalities involving history-dependent operators. For the problem, we first derive a semidiscrete scheme by implicit Euler formula and prove its unique solvability. The existence and uniqueness of a solution to the inequality problem is given by Rothe method. As the core part of the paper, we propose a two-step semidiscrete approximation for the problem, provide its unique solvability and obtain its second-order error estimates. The two-step scheme is more accurate than the standard implicit Euler scheme. Finally, we apply the results to a dynamic frictionless contact problem with long memory.Keywords: Hemivariational inequalitycontact problemhistory-dependent operatorerror estimatesMathematic Subject classifications: 65M1565N2274H15 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the European Unions Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grand Agreement No. 823731 CONMECH.
{"title":"Semidiscrete numerical approximation for dynamic hemivariational inequalities with history-dependent operators","authors":"Yujie Li, Xiaoliang Cheng, Hailing Xuan","doi":"10.1080/00036811.2023.2271031","DOIUrl":"https://doi.org/10.1080/00036811.2023.2271031","url":null,"abstract":"AbstractIn this paper, we are concerned with a class of second-order hemivariational inequalities involving history-dependent operators. For the problem, we first derive a semidiscrete scheme by implicit Euler formula and prove its unique solvability. The existence and uniqueness of a solution to the inequality problem is given by Rothe method. As the core part of the paper, we propose a two-step semidiscrete approximation for the problem, provide its unique solvability and obtain its second-order error estimates. The two-step scheme is more accurate than the standard implicit Euler scheme. Finally, we apply the results to a dynamic frictionless contact problem with long memory.Keywords: Hemivariational inequalitycontact problemhistory-dependent operatorerror estimatesMathematic Subject classifications: 65M1565N2274H15 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the European Unions Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grand Agreement No. 823731 CONMECH.","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135778380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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