This paper examines the existence of solutions to the continuous Redner-Ben-Avraham-Kahng coagulation system under specific growth conditions on unbounded coagulation kernels at infinity. Moreover, questions related to uniqueness and continuous dependence on the data are also addressed under additional restrictions. Finally, the large-time behaviour of solutions is also investigated
本文在无穷远无界混凝核上，研究了特定生长条件下连续redner - ben - avraham - kahn混凝体系解的存在性。此外，在附加的限制条件下，还讨论了与数据的唯一性和连续依赖性有关的问题。最后，还研究了解的大时态
{"title":"The continuous Redner-Ben-Avraham-Kahng coagulation system: Well-posedness and asymptotic behaviour","authors":"P. Verma, Ankik Kumar Giri, F. D. da Costa","doi":"10.3934/eect.2023010","DOIUrl":"https://doi.org/10.3934/eect.2023010","url":null,"abstract":"This paper examines the existence of solutions to the continuous Redner-Ben-Avraham-Kahng coagulation system under specific growth conditions on unbounded coagulation kernels at infinity. Moreover, questions related to uniqueness and continuous dependence on the data are also addressed under additional restrictions. Finally, the large-time behaviour of solutions is also investigated","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"8 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73174405","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}
{"title":"Numerical solution to the linearized model of a clamped-free plate using nonconforming finite elements","authors":"K. Szulc","doi":"10.3934/eect.2023020","DOIUrl":"https://doi.org/10.3934/eect.2023020","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"37 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73992027","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}
Abdelhadi Elharfi, Mustapha El Hassani, Samir El Mourchid
{"title":"Motion planning problem for a class of hyperbolic PDEs","authors":"Abdelhadi Elharfi, Mustapha El Hassani, Samir El Mourchid","doi":"10.3934/eect.2023011","DOIUrl":"https://doi.org/10.3934/eect.2023011","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"101 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80866575","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}
{"title":"A new class of small initial data which may shift the critical power and lifespan estimates for the classical damped wave equations","authors":"K. Fujiwara, V. Georgiev","doi":"10.3934/eect.2023003","DOIUrl":"https://doi.org/10.3934/eect.2023003","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"25 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81275180","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}
{"title":"Stabilization of a Rayleigh beam with collocated piezoelectric sensor/actuator","authors":"Yubo Bai, C. Prieur, Zhiqiang Wang","doi":"10.3934/eect.2023036","DOIUrl":"https://doi.org/10.3934/eect.2023036","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"301 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77203883","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}
{"title":"Stabilization for some degenerate wave equations","authors":"Guang Zhang, Shugen Chai","doi":"10.3934/eect.2023047","DOIUrl":"https://doi.org/10.3934/eect.2023047","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"65 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88618547","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}
This article concerns the long-term random dynamics for a non-autonomous Navier-Stokes equation defined on a bounded smooth domain $ mathcal{O} $ driven by multiplicative and additive noise. For the two kinds of noise driven equations, we demonstrate that the existence of a unique pullback attractor which is backward compact and asymptotically autonomous in $ mathbb{L}^2(mathcal{O}) $ and $ mathbb{H}_0^1(mathcal{O}) $, respectively. The compact embedding $ {mathbb{H}}_0^1(mathcal{O})subset{mathbb{L}}^2(mathcal{O}) $ helps us to show the backward-uniform pullback asymptotic compactness (BUPAC) of the non-autonomous random dynamical systems (NRDS) in the Lebesgue space $ {mathbb{L}}^2(mathcal{O}) $. The backward-uniform flattening property of the solutions is used to prove the BUPAC of the NRDS in the Sobolev space $ mathbb{H}_0^1(mathcal{O}) $.
{"title":"Asymptotic autonomy of random attractors for non-autonomous stochastic Navier-Stokes equations on bounded domains","authors":"Kush Kinra, Renhai Wang, Manil T. Mohan","doi":"10.3934/eect.2023049","DOIUrl":"https://doi.org/10.3934/eect.2023049","url":null,"abstract":"This article concerns the long-term random dynamics for a non-autonomous Navier-Stokes equation defined on a bounded smooth domain $ mathcal{O} $ driven by multiplicative and additive noise. For the two kinds of noise driven equations, we demonstrate that the existence of a unique pullback attractor which is backward compact and asymptotically autonomous in $ mathbb{L}^2(mathcal{O}) $ and $ mathbb{H}_0^1(mathcal{O}) $, respectively. The compact embedding $ {mathbb{H}}_0^1(mathcal{O})subset{mathbb{L}}^2(mathcal{O}) $ helps us to show the backward-uniform pullback asymptotic compactness (BUPAC) of the non-autonomous random dynamical systems (NRDS) in the Lebesgue space $ {mathbb{L}}^2(mathcal{O}) $. The backward-uniform flattening property of the solutions is used to prove the BUPAC of the NRDS in the Sobolev space $ mathbb{H}_0^1(mathcal{O}) $.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"192 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135496188","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}
{"title":"An anisotropic tempered fractional $ p $-Laplacian model involving logarithmic nonlinearity","authors":"Lihong Zhang, Wenwen Hou, J. Nieto, Guotao Wang","doi":"10.3934/eect.2023033","DOIUrl":"https://doi.org/10.3934/eect.2023033","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72713187","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}
In this paper we establish some regularity results concerning the behavior of weak solutions and very weak solutions of the degenerate wave equation near the boundary. For the nondegenerate case, the correponding results were originally obtained by Fabre and Puel (J. of Diff. Eq. 106, 1993). This kind of results is closely related to the exact boundary controllability for the wave equation as the limit of internal controllability.
本文建立了简并波动方程在边界附近弱解和甚弱解行为的一些规律性结果。对于非简并情况，相应的结果最初由Fabre和Puel (J. of Diff. Eq. 106, 1993)得出。这种结果与波动方程作为内部可控性极限的精确边界可控性密切相关。
{"title":"Regularity results for degenerate wave equations in a neighborhood of the boundary","authors":"Bruno S. V. Ara'ujo, R. Demarque, L. Viana","doi":"10.3934/eect.2023013","DOIUrl":"https://doi.org/10.3934/eect.2023013","url":null,"abstract":"In this paper we establish some regularity results concerning the behavior of weak solutions and very weak solutions of the degenerate wave equation near the boundary. For the nondegenerate case, the correponding results were originally obtained by Fabre and Puel (J. of Diff. Eq. 106, 1993). This kind of results is closely related to the exact boundary controllability for the wave equation as the limit of internal controllability.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"91 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84414155","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}
Salah-Eddine Chorfi, G. E. Guermai, A. Khoutaibi, L. Maniar
In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control supported on an arbitrary subboundary. The proof of the main result combines a new boundary Carleman estimate and some regularity estimates for the adjoint system, with an explicit dependence with respect to the final time. This technique allows us to overcome a new difficulty that arises when absorbing a normal derivative term.
{"title":"Boundary null controllability for the heat equation with dynamic boundary conditions","authors":"Salah-Eddine Chorfi, G. E. Guermai, A. Khoutaibi, L. Maniar","doi":"10.3934/eect.2022041","DOIUrl":"https://doi.org/10.3934/eect.2022041","url":null,"abstract":"In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control supported on an arbitrary subboundary. The proof of the main result combines a new boundary Carleman estimate and some regularity estimates for the adjoint system, with an explicit dependence with respect to the final time. This technique allows us to overcome a new difficulty that arises when absorbing a normal derivative term.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"40 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73063269","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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