Advances in Nonlinear Analysis最新文献_第9页

On Cauchy problem for fractional parabolic-elliptic Keller-Segel model 分数阶抛物-椭圆Keller-Segel模型的Cauchy问题

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-08-22 DOI: 10.1515/anona-2022-0256

A. Nguyen, N. Tuan, Chao Yang

{"title":"On Cauchy problem for fractional parabolic-elliptic Keller-Segel model","authors":"A. Nguyen, N. Tuan, Chao Yang","doi":"10.1515/anona-2022-0256","DOIUrl":"https://doi.org/10.1515/anona-2022-0256","url":null,"abstract":"Abstract In this paper, we concern about a modified version of the Keller-Segel model. The Keller-Segel is a system of partial differential equations used for modeling Chemotaxis in which chemical substances impact the movement of mobile species. For considering memory effects on the model, we replace the classical derivative with respect to time variable by the time-fractional derivative in the sense of Caputo. From this modification, we focus on the well-posedness of the Cauchy problem associated with such the model. Precisely, when the spatial variable is considered in the space R d {{mathbb{R}}}^{d} , a global solution is obtained in a critical homogeneous Besov space with the assumption that the initial datum is sufficiently small. For the bounded domain case, by using a discrete spectrum of the Neumann Laplace operator, we provide the existence and uniqueness of a mild solution in Hilbert scale spaces. Moreover, the blowup behavior is also studied. To overcome the challenges of the problem and obtain all the aforementioned results, we use the Banach fixed point theorem, some special functions like the Mainardi function and the Mittag-Leffler function, as well as their properties.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41684866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 16

On regular solutions to compressible radiation hydrodynamic equations with far field vacuum 带远场真空的可压缩辐射流体动力学方程的正则解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-08-20 DOI: 10.1515/anona-2022-0264

Hao Li, Shengguo Zhu

{"title":"On regular solutions to compressible radiation hydrodynamic equations with far field vacuum","authors":"Hao Li, Shengguo Zhu","doi":"10.1515/anona-2022-0264","DOIUrl":"https://doi.org/10.1515/anona-2022-0264","url":null,"abstract":"Abstract The Cauchy problem for three-dimensional (3D) isentropic compressible radiation hydrodynamic equations is considered. When both shear and bulk viscosity coefficients depend on the mass density ρ rho in a power law ρ δ {rho }^{delta } (with 0 < δ < 1 0lt delta lt 1 ), based on some elaborate analysis of this system’s intrinsic singular structures, we establish the local-in-time well-posedness of regular solution with arbitrarily large initial data and far field vacuum in some inhomogeneous Sobolev spaces by introducing some new variables and initial compatibility conditions. Note that due to the appearance of the vacuum, the momentum equations are degenerate both in the time evolution and viscous stress tensor, which, along with the strong coupling between the fluid and the radiation field, make the study on corresponding well-posedness challenging. For proving the existence, we first introduce an enlarged reformulated structure by considering some new variables, which can transfer the degeneracies of the radiation hydrodynamic equations to the possible singularities of some special source terms, and then carry out some singularly weighted energy estimates carefully designed for this reformulated system.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44673197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Identification of discontinuous parameters in double phase obstacle problems 双相障碍问题中不连续参数的辨识

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-08-19 DOI: 10.1515/anona-2022-0223

Shengda Zeng, Yunru Bai, Patrick Winkert, J. Yao

引用次数: 2

Global boundedness to a 3D chemotaxis-Stokes system with porous medium cell diffusion and general sensitivity 具有多孔介质-细胞扩散和一般灵敏度的三维趋化性Stokes系统的全局有界性

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-08-19 DOI: 10.1515/anona-2022-0228

Yu Tian, Zhaoyin Xiang

引用次数: 2

On a system of multi-component Ginzburg-Landau vortices 关于多分量金兹堡-朗道涡系统

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-05-29 DOI: 10.1515/anona-2022-0315

R. Hadiji, Jongmin Han, Juhee Sohn

引用次数: 0

On the fractional Korn inequality in bounded domains: Counterexamples to the case ps < 1 关于有界域中的分数Korn不等式：情形ps的反例 < 1.

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-04-03 DOI: 10.1515/anona-2022-0283

D. Harutyunyan, H. Mikayelyan

{"title":"On the fractional Korn inequality in bounded domains: Counterexamples to the case ps < 1","authors":"D. Harutyunyan, H. Mikayelyan","doi":"10.1515/anona-2022-0283","DOIUrl":"https://doi.org/10.1515/anona-2022-0283","url":null,"abstract":"Abstract The validity of Korn’s first inequality in the fractional setting in bounded domains has been open. We resolve this problem by proving that in fact Korn’s first inequality holds in the case p s > 1 psgt 1 for fractional W 0 s , p ( Ω ) {W}_{0}^{s,p}left(Omega ) Sobolev fields in open and bounded C 1 {C}^{1} -regular domains Ω ⊂ R n Omega subset {{mathbb{R}}}^{n} . Also, in the case p s < 1 pslt 1 , for any open bounded C 1 {C}^{1} domain Ω ⊂ R n Omega subset {{mathbb{R}}}^{n} , we construct counterexamples to the inequality, i.e., Korn’s first inequality fails to hold in bounded domains. The proof of the inequality in the case p s > 1 psgt 1 follows a standard compactness approach adopted in the classical case, combined with a Hardy inequality, and a recently proven Korn second inequality by Mengesha and Scott [A Fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations, Commun. Math. Sci. 20 (2022), no. 2, 405–423]. The counterexamples constructed in the case p s < 1 pslt 1 are interpolations of a constant affine rigid motion inside the domain away from the boundary and of the zero field close to the boundary.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43672152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

On sufficient “local” conditions for existence results to generalized p(.)-Laplace equations involving critical growth 关于存在的充分“局部”条件，得到了涉及临界增长的广义p(.)-拉普拉斯方程的结果

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-28 DOI: 10.1515/anona-2022-0269

Ky Ho, Inbo Sim

引用次数: 0

Non-local gradients in bounded domains motivated by continuum mechanics: Fundamental theorem of calculus and embeddings 连续介质力学驱动的有界域中的非局部梯度：微积分和嵌入的基本定理

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-21 DOI: 10.1515/anona-2022-0316

J. C. Bellido, J. Cueto, C. Mora-Corral

{"title":"Non-local gradients in bounded domains motivated by continuum mechanics: Fundamental theorem of calculus and embeddings","authors":"J. C. Bellido, J. Cueto, C. Mora-Corral","doi":"10.1515/anona-2022-0316","DOIUrl":"https://doi.org/10.1515/anona-2022-0316","url":null,"abstract":"Abstract In this article, we develop a new set of results based on a non-local gradient jointly inspired by the Riesz s s -fractional gradient and peridynamics, in the sense that its integration domain depends on a ball of radius δ > 0 delta gt 0 (horizon of interaction among particles, in the terminology of peridynamics), while keeping at the same time the singularity of the Riesz potential in its integration kernel. Accordingly, we define a functional space suitable for non-local models in calculus of variations and partial differential equations. Our motivation is to develop the proper functional analysis framework to tackle non-local models in continuum mechanics, which requires working with bounded domains, while retaining the good mathematical properties of Riesz s s -fractional gradients. This functional space is defined consistently with Sobolev and Bessel fractional ones: we consider the closure of smooth functions under the natural norm obtained as the sum of the L p {L}^{p} norms of the function and its non-local gradient. Among the results showed in this investigation, we highlight a non-local version of the fundamental theorem of calculus (namely, a representation formula where a function can be recovered from its non-local gradient), which allows us to prove inequalities in the spirit of Poincaré, Morrey, Trudinger, and Hardy as well as the corresponding compact embeddings. These results are enough to show the existence of minimizers of general energy functionals under the assumption of convexity. Equilibrium conditions in this non-local situation are also established, and those can be viewed as a new class of non-local partial differential equations in bounded domains.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2022-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43151875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 7

Global attractors of the degenerate fractional Kirchhoff wave equation with structural damping or strong damping 具有结构阻尼或强阻尼的退化分数Kirchhoff波动方程的全局吸引子

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0226

Wenhua Yang, Jun Zhou

引用次数: 6

Constrained optimization problems governed by PDE models of grain boundary motions 晶界运动PDE模型控制的约束优化问题

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0242

Harbir Antil, Shodai Kubota, K. Shirakawa, N. Yamazaki

引用次数: 0