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Evolution Equations and Control Theory最新文献

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Uniform stabilization for a string/point mass system via arbitrary local memory effects versus frictional damping 通过任意局部记忆效应与摩擦阻尼实现串/点质量系统的均匀稳定
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022056
Kun‐Peng Jin, Chan Li
{"title":"Uniform stabilization for a string/point mass system via arbitrary local memory effects versus frictional damping","authors":"Kun‐Peng Jin, Chan Li","doi":"10.3934/eect.2022056","DOIUrl":"https://doi.org/10.3934/eect.2022056","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88220065","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}
引用次数: 0
A note on control of one-dimensional heterogeneous reaction-diffusion equations 一维非均相反应扩散方程的控制问题
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022035
M. Sônego, R. Roychowdhury
{"title":"A note on control of one-dimensional heterogeneous reaction-diffusion equations","authors":"M. Sônego, R. Roychowdhury","doi":"10.3934/eect.2022035","DOIUrl":"https://doi.org/10.3934/eect.2022035","url":null,"abstract":"<p style='text-indent:20px;'>We are concerned with the controllability of a general heterogeneous semilinear parabolic equation of the form <inline-formula><tex-math id=\"M1\">begin{document}$ y_t(x,t)=y_{xx}(x,t)+f(x,y(x,t)) $end{document}</tex-math></inline-formula> in one space dimension using boundary static controls. More precisely, we provide conditions so that, using only static controls at the boundary, a certain target (a steady-state of the equation) is reached in infinite time. Applications of the main result are also presented, in particular, we provide several controllability results to heterogeneous equations of monostable and bistable types.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"16 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82544633","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}
引用次数: 0
Time periodic solution to chemotaxis-shallow water system in a periodic domain 趋化-浅水系统周期域的时间周期解
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022044
Qingfang Shi, Xinli Zhang
{"title":"Time periodic solution to chemotaxis-shallow water system in a periodic domain","authors":"Qingfang Shi, Xinli Zhang","doi":"10.3934/eect.2022044","DOIUrl":"https://doi.org/10.3934/eect.2022044","url":null,"abstract":"In this paper, we analyse the existence and uniqueness of a time-periodic solution to chemotaxis-shallow water system in a periodic domain. Under the assumption of some smallness and symmetric external force, the existence of periodic solution is established using the method of parabolic regularization and limit process. The uniqueness of the periodic solution is proved by energy estimates.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89213477","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}
引用次数: 1
Inverse problems for anisotropic obstacle problems with multivalued convection and unbalanced growth 具有多值对流和不平衡生长的各向异性障碍问题的逆问题
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022051
Shengda Zeng, Yunru Bai, Vicenţiu D. Rădulescu
{"title":"Inverse problems for anisotropic obstacle problems with multivalued convection and unbalanced growth","authors":"Shengda Zeng, Yunru Bai, Vicenţiu D. Rădulescu","doi":"10.3934/eect.2022051","DOIUrl":"https://doi.org/10.3934/eect.2022051","url":null,"abstract":"<p style='text-indent:20px;'>The prime goal of this paper is to introduce and study a highly nonlinear inverse problem of identification discontinuous parameters (in the domain) and boundary data in a nonlinear variable exponent elliptic obstacle problem involving a nonhomogeneous, nonlinear partial differential operator, which is formulated the sum of a weighted anisotropic <inline-formula><tex-math id=\"M1\">begin{document}$ p $end{document}</tex-math></inline-formula>-Laplacian and a weighted anisotropic <inline-formula><tex-math id=\"M2\">begin{document}$ q $end{document}</tex-math></inline-formula>-Laplacian (called the weighted anisotropic <inline-formula><tex-math id=\"M3\">begin{document}$ (p,q) $end{document}</tex-math></inline-formula>-Laplacian), a multivalued reaction term depending on the gradient, two multivalued boundary conditions and an obstacle constraint. We, first, employ the theory of nonsmooth analysis and a surjectivity theorem for pseudomonotone operators to prove the existence of a nontrivial solution of the anisotropic elliptic obstacle problem, which relies on the first eigenvalue of the Steklov eigenvalue problem for the <inline-formula><tex-math id=\"M4\">begin{document}$ p_$end{document}</tex-math></inline-formula>-Laplacian. Then, we introduce the parameter-to-solution map for the anisotropic elliptic obstacle problem, and establish a critical convergence result of the Kuratowski type to parameter-to-solution map. Finally, a general framework is proposed to examine the solvability of the nonlinear inverse problem.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"133 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73836430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Time periodic solution to a mechanochemical model in biological patterns 生物模式中机械化学模型的时间周期解
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022039
Chengxin Du, Changchun Liu
{"title":"Time periodic solution to a mechanochemical model in biological patterns","authors":"Chengxin Du, Changchun Liu","doi":"10.3934/eect.2022039","DOIUrl":"https://doi.org/10.3934/eect.2022039","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we consider a mechanochemical model in biological patterns in <inline-formula><tex-math id=\"M1\">begin{document}$ mathbb{R}^N $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M2\">begin{document}$ Ngeq 5 $end{document}</tex-math></inline-formula>. We first prove the existence of time periodic solution in <inline-formula><tex-math id=\"M3\">begin{document}$ BC(mathbb{R}; L^{N,infty}(Omega)) $end{document}</tex-math></inline-formula>. Then we obtain the existence, uniqueness and regularity of the mild solution of the problem. Finally, we prove that the mild solution can become strong solution in <inline-formula><tex-math id=\"M4\">begin{document}$ BC(mathbb{R}; L^{N,infty}(Omega)) $end{document}</tex-math></inline-formula>.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"13 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74902982","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}
引用次数: 0
Asymptotic analysis of an age-structured predator-prey model with ratio-dependent Holling Ⅲ functional response and delays 具有比例依赖HollingⅢ功能反应和延迟的年龄结构捕食者-猎物模型的渐近分析
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022034
Dongxue Yan, Yuan Yuan, Xianlong Fu
{"title":"Asymptotic analysis of an age-structured predator-prey model with ratio-dependent Holling Ⅲ functional response and delays","authors":"Dongxue Yan, Yuan Yuan, Xianlong Fu","doi":"10.3934/eect.2022034","DOIUrl":"https://doi.org/10.3934/eect.2022034","url":null,"abstract":"This paper studies the dynamical behavior of a radio-dependent predator-prey model with age structure and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the conditions for existence of the positive equilibrium point are derived. Then, through determining the distribution of eigenvalues, the globally asymptotic stability of the boundary equilibrium and the locally asymptotic stability for the positive equilibrium are obtained, respectively. In addition, it is also shown that a non-trivial periodic oscillation phenomenon through Hopf bifurcation appears under some conditions. Finally, some numerical examples are provided to illustrate the obtained results.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"52 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76511483","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}
引用次数: 1
Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions 非单调边界条件下弹粘塑性动态接触问题的连续依赖与最优控制
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2021064
Xilu Wang, Xiaoliang Cheng
{"title":"Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions","authors":"Xilu Wang, Xiaoliang Cheng","doi":"10.3934/eect.2021064","DOIUrl":"https://doi.org/10.3934/eect.2021064","url":null,"abstract":"In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"3 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87575137","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}
引用次数: 1
On the well-posedness of a tensor-based second order PDE with bilateral term for image super-resolution 基于张量的二阶双侧偏微分方程的超分辨率适定性
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022047
El Mourabit Idriss, A. Hakim, A. Laghrib
{"title":"On the well-posedness of a tensor-based second order PDE with bilateral term for image super-resolution","authors":"El Mourabit Idriss, A. Hakim, A. Laghrib","doi":"10.3934/eect.2022047","DOIUrl":"https://doi.org/10.3934/eect.2022047","url":null,"abstract":"In this paper, we introduce a second-order equation based on a diffusion tensor combined with a bilateral total variation (BTV) term that takes the benefit from the diffusion model of Perona-Malik in the homogeneous regions, the Weickert model near sharp edge and the BTV term in reducing blur. Compared to the other partial differential equations (PDE) used in the SR context, the proposed super-resolution (SR) PDE can efficiently preserve image components such as corners and flat regions with less apparition of blur in homogeneous regions. Moreover, since the SR approaches are always ill-posed, a mathematical study of the existence and uniqueness of the solution is also checked in a Sobolev space. From the numerical experiments we can observe that the proposed PDE can efficiently improve the quality of the high-resolution (HR) image. Surprisingly, the apparition of blur in the restored image is less compared to the other methods. In addition to visual evaluation, two-based metrics are computed to confirm the improvements offered by the proposed PDE.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"24 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82733620","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}
引用次数: 2
Controllability of retarded time-dependent neutral stochastic integro-differential systems driven by fractional Brownian motion 分数布朗运动驱动的时滞时变中性随机积分微分系统的可控性
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022031
Youssef Benkabdi, E. Lakhel
{"title":"Controllability of retarded time-dependent neutral stochastic integro-differential systems driven by fractional Brownian motion","authors":"Youssef Benkabdi, E. Lakhel","doi":"10.3934/eect.2022031","DOIUrl":"https://doi.org/10.3934/eect.2022031","url":null,"abstract":"In this manuscript the controllability for a class of time-dependent neutral stochastic integro-differential systems driven by fractional Brownian motion in a separable Hilbert space with delay is studied. The controllability result is obtained by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"35 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82657240","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}
引用次数: 1
Controllability of Hilfer type fractional evolution neutral integro-differential inclusions with non-instantaneous impulses 非瞬时脉冲Hilfer型分数演化中性积分微分包体的可控性
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022043
K. Sanjay, P. Balasubramaniam
{"title":"Controllability of Hilfer type fractional evolution neutral integro-differential inclusions with non-instantaneous impulses","authors":"K. Sanjay, P. Balasubramaniam","doi":"10.3934/eect.2022043","DOIUrl":"https://doi.org/10.3934/eect.2022043","url":null,"abstract":"In this manuscript the controllability of Hilfer fractional neutral differential inclusions with non-instantaneous impulse in Banach space is investigated by using semi-group theory, fractional calculus, upper semi-continuous (u.s.c), multi-functions and Mönch fixed point theorem. Sufficient conditions are derived by using Hausdorff measure of non-compactness (MNC). Further, the obtained result is illustrated by an example.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"73 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86391180","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}
引用次数: 1
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