Pub Date : 2021-11-09DOI: 10.1142/s0219530521500184
Yi-Long Luo, Yangjun Ma
The Qian–Sheng model is a system describing the hydrodynamics of nematic liquid crystals in the Q-tensor framework. When the inertial effect is included, it is a hyperbolic-type system involving a second-order material derivative coupling with forced incompressible Navier–Stokes equations. If formally letting the inertial constant [Formula: see text] go to zero, the resulting system is the corresponding parabolic model. We provide the result on the rigorous justification of this limit in [Formula: see text] with small initial data, which validates mathematically the parabolic Qian–Sheng model. To achieve this, an initial layer is introduced to not only overcome the disparity of the initial conditions between the hyperbolic and parabolic models, but also make the convergence rate optimal. Moreover, a novel [Formula: see text]-dependent energy norm is carefully designed, which is non-negative only when [Formula: see text] is small enough, and handles the difficulty brought by the second-order material derivative.
{"title":"Zero inertia limit of incompressible Qian–Sheng model","authors":"Yi-Long Luo, Yangjun Ma","doi":"10.1142/s0219530521500184","DOIUrl":"https://doi.org/10.1142/s0219530521500184","url":null,"abstract":"The Qian–Sheng model is a system describing the hydrodynamics of nematic liquid crystals in the Q-tensor framework. When the inertial effect is included, it is a hyperbolic-type system involving a second-order material derivative coupling with forced incompressible Navier–Stokes equations. If formally letting the inertial constant [Formula: see text] go to zero, the resulting system is the corresponding parabolic model. We provide the result on the rigorous justification of this limit in [Formula: see text] with small initial data, which validates mathematically the parabolic Qian–Sheng model. To achieve this, an initial layer is introduced to not only overcome the disparity of the initial conditions between the hyperbolic and parabolic models, but also make the convergence rate optimal. Moreover, a novel [Formula: see text]-dependent energy norm is carefully designed, which is non-negative only when [Formula: see text] is small enough, and handles the difficulty brought by the second-order material derivative.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44958695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-09DOI: 10.1142/s0219530523500100
Xinchi Huang, Yavar Kian, É. Soccorsi, Masahiro Yamamoto
We consider the inverse problem of determining the initial states or the source term of a hyperbolic equation damped by some non-local time-fractional derivative. This framework is relevant to medical imaging such as thermoacoustic or photoacoustic tomography. We prove a stability estimate for each of these two problems, with the aid of a Carleman estimate specifically designed for the governing equation.
{"title":"Determination of source or initial values for acoustic equations with a time-fractional attenuation","authors":"Xinchi Huang, Yavar Kian, É. Soccorsi, Masahiro Yamamoto","doi":"10.1142/s0219530523500100","DOIUrl":"https://doi.org/10.1142/s0219530523500100","url":null,"abstract":"We consider the inverse problem of determining the initial states or the source term of a hyperbolic equation damped by some non-local time-fractional derivative. This framework is relevant to medical imaging such as thermoacoustic or photoacoustic tomography. We prove a stability estimate for each of these two problems, with the aid of a Carleman estimate specifically designed for the governing equation.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47846859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-07DOI: 10.1142/s0219530523500057
J. Betancor, M. D. Le'on-Contreras
In this paper we establish $L^p$-boundedness properties for variation, oscillation and jump operators associated with Riesz transforms and Poisson semigroups related to Laguerre polynomial expansions.
{"title":"Variation inequalities for riesz transforms and poisson semigroups associated with laguerre polynomial expansions","authors":"J. Betancor, M. D. Le'on-Contreras","doi":"10.1142/s0219530523500057","DOIUrl":"https://doi.org/10.1142/s0219530523500057","url":null,"abstract":"In this paper we establish $L^p$-boundedness properties for variation, oscillation and jump operators associated with Riesz transforms and Poisson semigroups related to Laguerre polynomial expansions.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49199135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-06DOI: 10.1142/s0219530521500238
Shousheng Luo, X. Tai, Yang Wang
{"title":"A New Binary Representation Method for Shape Convexity and Application to Image Segmentation","authors":"Shousheng Luo, X. Tai, Yang Wang","doi":"10.1142/s0219530521500238","DOIUrl":"https://doi.org/10.1142/s0219530521500238","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41919034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-06DOI: 10.1142/s0219530521500251
W. Qu, C. Chui, Guantie Deng, T. Qian
{"title":"Sparse Representation of Approximation to Identity","authors":"W. Qu, C. Chui, Guantie Deng, T. Qian","doi":"10.1142/s0219530521500251","DOIUrl":"https://doi.org/10.1142/s0219530521500251","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41465657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-06DOI: 10.1142/s0219530521500214
Guangqing Wang, Wenyi Chen, Jie Yang
{"title":"On the Global L∞→BMO Mapping Property for Fourier Integral Operators","authors":"Guangqing Wang, Wenyi Chen, Jie Yang","doi":"10.1142/s0219530521500214","DOIUrl":"https://doi.org/10.1142/s0219530521500214","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46324009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-23DOI: 10.1142/s0219530521500172
Xiuwei Yin, Guangjun Shen, Jiang-Lun Wu
In this paper, we study the stability of quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The exponential mean square stability and pathwise exponential stability of the solutions are established. Moreover, under certain hypothesis on the stochastic perturbations, pathwise exponential stability can be derived, without utilizing the mean square stability.
{"title":"The exponential behavior and stabilizability of quasilinear parabolic stochastic partial differential equation","authors":"Xiuwei Yin, Guangjun Shen, Jiang-Lun Wu","doi":"10.1142/s0219530521500172","DOIUrl":"https://doi.org/10.1142/s0219530521500172","url":null,"abstract":"In this paper, we study the stability of quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The exponential mean square stability and pathwise exponential stability of the solutions are established. Moreover, under certain hypothesis on the stochastic perturbations, pathwise exponential stability can be derived, without utilizing the mean square stability.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41975925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-04DOI: 10.1142/s0219530521500159
A. Ito
This paper deals with a nonlinear system (S) composed of three PDEs and one ODE below: [Formula: see text] The system (S) was proposed as one of the mathematical models which describe tumor invasion phenomena with chemotaxis effects. The most important and interesting point is that the diffusion coefficient of tumor cells, denoted by [Formula: see text], is influenced by both nonlocal effect of a chemical attractive substance, denoted by [Formula: see text], and the local one of extracellular matrix, denoted by [Formula: see text]. From this point, the first PDE in (S) contains a nonlinear cross diffusion. Actually, this mathematical setting gives an inner product of a suitable real Hilbert space, which governs the dynamics of the density of tumor cells [Formula: see text], a quasi-variational structure. Hence, the first purpose in this paper is to make it clear what this real Hilbert space is. After this, we show the existence of strong time local solutions to the initial-boundary problems associated with (S) when the space dimension is [Formula: see text] by applying the general theory of evolution inclusions on real Hilbert spaces with quasi-variational structures. Moreover, for the case [Formula: see text] we succeed in constructing a strong time global solution.
{"title":"A mass-conserved tumor invasion system with quasi-variational degenerate diffusion","authors":"A. Ito","doi":"10.1142/s0219530521500159","DOIUrl":"https://doi.org/10.1142/s0219530521500159","url":null,"abstract":"This paper deals with a nonlinear system (S) composed of three PDEs and one ODE below: [Formula: see text] The system (S) was proposed as one of the mathematical models which describe tumor invasion phenomena with chemotaxis effects. The most important and interesting point is that the diffusion coefficient of tumor cells, denoted by [Formula: see text], is influenced by both nonlocal effect of a chemical attractive substance, denoted by [Formula: see text], and the local one of extracellular matrix, denoted by [Formula: see text]. From this point, the first PDE in (S) contains a nonlinear cross diffusion. Actually, this mathematical setting gives an inner product of a suitable real Hilbert space, which governs the dynamics of the density of tumor cells [Formula: see text], a quasi-variational structure. Hence, the first purpose in this paper is to make it clear what this real Hilbert space is. After this, we show the existence of strong time local solutions to the initial-boundary problems associated with (S) when the space dimension is [Formula: see text] by applying the general theory of evolution inclusions on real Hilbert spaces with quasi-variational structures. Moreover, for the case [Formula: see text] we succeed in constructing a strong time global solution.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44678841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-03DOI: 10.1142/S021953052350001X
E. Galapon
. Finite-part integration is a recent method of evaluating a convergent integral in terms of the finite-parts of divergent integrals deliberately in- duced from the convergent integral itself [E. A. Galapon, Proc. R. Soc., A 473, 20160567 (2017)]. Within the context of finite-part integration of the Stieltjes transform of functions with logarithmic growths at the origin, the relationship is established between the analytic continuation of the Mellin transform and the finite-part of the resulting divergent integral when the Mellin integral is extended beyond its strip of analyticity. It is settled that the analytic continu- ation and the finite-part integral coincide at the regular points of the analytic continuation. To establish the connection between the two at the isolated singularities of the analytic continuation, the concept of regularized limit is introduced to replace the usual concept of limit due to Cauchy when the later leads to a division by zero. It is then shown that the regularized limit of the analytic continuation at its isolated singularities equals the finite-part integrals at the singularities themselves. The treatment gives the exact evaluation of the Stieltjes transform in terms of finite-part integrals and yields the domi- nant asymptotic behavior of the transform for arbitrarily small values of the parameter in the presence of arbitrary logarithmic singularities at the origin.
． 有限部分积分是一种用发散积分的有限部分来计算收敛积分的新方法[E]。A. Galapon, Proc. R. Soc。[j].农业工程学报，2016,37(4):20160567(2017)。在原点具有对数增长的函数的Stieltjes变换的有限部分积分的背景下，当Mellin积分扩展到其可解析性范围之外时，建立了Mellin变换的解析延拓与结果发散积分的有限部分之间的关系。证明了解析延拓与有限部分积分在解析延拓的正则点重合。为了在解析延拓的孤立奇点处建立两者之间的联系，引入正则化极限的概念来代替通常的柯西极限概念，当后者导致除零时。然后证明了解析延拓在孤立奇异点处的正则化极限等于奇异点处的有限部分积分。该处理给出了Stieltjes变换在有限部分积分中的精确计算，并给出了在原点存在任意对数奇点时，对于参数的任意小值，该变换的主导渐近性质。
{"title":"Regularized Limit, Analytic Continuation and Finite-part Integration","authors":"E. Galapon","doi":"10.1142/S021953052350001X","DOIUrl":"https://doi.org/10.1142/S021953052350001X","url":null,"abstract":". Finite-part integration is a recent method of evaluating a convergent integral in terms of the finite-parts of divergent integrals deliberately in- duced from the convergent integral itself [E. A. Galapon, Proc. R. Soc., A 473, 20160567 (2017)]. Within the context of finite-part integration of the Stieltjes transform of functions with logarithmic growths at the origin, the relationship is established between the analytic continuation of the Mellin transform and the finite-part of the resulting divergent integral when the Mellin integral is extended beyond its strip of analyticity. It is settled that the analytic continu- ation and the finite-part integral coincide at the regular points of the analytic continuation. To establish the connection between the two at the isolated singularities of the analytic continuation, the concept of regularized limit is introduced to replace the usual concept of limit due to Cauchy when the later leads to a division by zero. It is then shown that the regularized limit of the analytic continuation at its isolated singularities equals the finite-part integrals at the singularities themselves. The treatment gives the exact evaluation of the Stieltjes transform in terms of finite-part integrals and yields the domi- nant asymptotic behavior of the transform for arbitrarily small values of the parameter in the presence of arbitrary logarithmic singularities at the origin.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43924335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-26DOI: 10.1142/s0219530521500147
M. Melgaard, F. Zongo
We study the nonlinear, nonlocal, time-dependent partial differential equation [Formula: see text] which is known to describe the dynamics of quasi-relativistic boson stars in the mean-field limit. For positive mass parameter [Formula: see text] we establish existence of infinitely many (corresponding to distinct energies [Formula: see text]) traveling solitary waves, [Formula: see text], with speed [Formula: see text], where [Formula: see text] corresponds to the speed of light in our choice of units. These traveling solitary waves cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with [Formula: see text]) because Lorentz covariance fails. Instead, we study a suitable variational problem for which the functions [Formula: see text] arise as solutions (called boosted excited states) to a Choquard-type equation in [Formula: see text], where the negative Laplacian is replaced by the pseudo-differential operator [Formula: see text] and an additional term [Formula: see text] enters. Moreover, we give a new proof for existence of boosted ground states. The results are based on perturbation methods in critical point theory.
{"title":"Solitary waves and excited states for Boson stars","authors":"M. Melgaard, F. Zongo","doi":"10.1142/s0219530521500147","DOIUrl":"https://doi.org/10.1142/s0219530521500147","url":null,"abstract":"We study the nonlinear, nonlocal, time-dependent partial differential equation [Formula: see text] which is known to describe the dynamics of quasi-relativistic boson stars in the mean-field limit. For positive mass parameter [Formula: see text] we establish existence of infinitely many (corresponding to distinct energies [Formula: see text]) traveling solitary waves, [Formula: see text], with speed [Formula: see text], where [Formula: see text] corresponds to the speed of light in our choice of units. These traveling solitary waves cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with [Formula: see text]) because Lorentz covariance fails. Instead, we study a suitable variational problem for which the functions [Formula: see text] arise as solutions (called boosted excited states) to a Choquard-type equation in [Formula: see text], where the negative Laplacian is replaced by the pseudo-differential operator [Formula: see text] and an additional term [Formula: see text] enters. Moreover, we give a new proof for existence of boosted ground states. The results are based on perturbation methods in critical point theory.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46417594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：