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Spectrum, bifurcation and hypersurfaces of prescribed k-th mean curvature in Minkowski space 闵可夫斯基空间中规定k次平均曲率的谱、分岔和超曲面
4区 数学
Asymptotic Analysis Pub Date : 2023-11-10 DOI: 10.3233/asy-231877
Guowei Dai, Zhitao Zhang
{"title":"Spectrum, bifurcation and hypersurfaces of prescribed k-th mean curvature in Minkowski space","authors":"Guowei Dai, Zhitao Zhang","doi":"10.3233/asy-231877","DOIUrl":"https://doi.org/10.3233/asy-231877","url":null,"abstract":"By bifurcation and topological methods, we study the existence/nonexistence and multiplicity of one-sign or nodal solutions of the following k-th mean curvature problem in Minkowski spacetime r N − k v ′ 1 − v ′ 2 k ′ = λ N C N k r N − 1 H k ( r , v ) in ( 0 , R ) , | v ′ | < 1 in ( 0 , R ) , v ′ ( 0 ) = v ( R ) = 0 . As a previous step, we investigate the spectral structure of its linearized problem at zero. Moreover, we also obtain a priori bounds and the asymptotic behaviors of solutions with respect to λ.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135137212","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
Existence results for the Landau–Lifshitz–Baryakhtar equation Landau-Lifshitz-Baryakhtar方程的存在性结果
4区 数学
Asymptotic Analysis Pub Date : 2023-11-10 DOI: 10.3233/asy-231874
C. Ayouch, D. Meskine, M. Tilioua
{"title":"Existence results for the Landau–Lifshitz–Baryakhtar equation","authors":"C. Ayouch, D. Meskine, M. Tilioua","doi":"10.3233/asy-231874","DOIUrl":"https://doi.org/10.3233/asy-231874","url":null,"abstract":"In this paper, the Landau–Lifshitz–Baryakhtar (LLBar) equation for magnetization dynamics in ferrimagnets is considered. We prove global existence of a periodic solutions as well as local existence and uniqueness of regular solutions. We also study the relationships between the Landau–Lifshitz–Baryakhtar equation and both Landau–Lifshitz–Bloch and harmonic map equations.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135137217","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
The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary 将动态边界条件作为边界退化问题的奇异极限的热方程
4区 数学
Asymptotic Analysis Pub Date : 2023-11-10 DOI: 10.3233/asy-231862
Yoshikazu Giga, Michał Łasica, Piotr Rybka
{"title":"The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary","authors":"Yoshikazu Giga, Michał Łasica, Piotr Rybka","doi":"10.3233/asy-231862","DOIUrl":"https://doi.org/10.3233/asy-231862","url":null,"abstract":"We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the layer tends to zero. We also discuss Γ-convergence of the functionals generating these flows. Our analysis of strong solutions depends on a new version of the Reilly identity.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087348","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
The Euler–Poisswell/Darwin equation and the asymptotic hierarchy of the Euler–Maxwell equation 欧拉-泊斯威尔/达尔文方程和欧拉-麦克斯韦方程的渐近层次
4区 数学
Asymptotic Analysis Pub Date : 2023-11-10 DOI: 10.3233/asy-231864
Jakob Möller, Norbert J. Mauser
{"title":"The Euler–Poisswell/Darwin equation and the asymptotic hierarchy of the Euler–Maxwell equation","authors":"Jakob Möller, Norbert J. Mauser","doi":"10.3233/asy-231864","DOIUrl":"https://doi.org/10.3233/asy-231864","url":null,"abstract":"In this paper we introduce the (unipolar) pressureless Euler–Poisswell equation for electrons as the O ( 1 / c ) semi-relativistic approximation and the (unipolar) pressureless Euler–Darwin equation as the O ( 1 / c 2 ) semi-relativistic approximation of the (unipolar) pressureless Euler–Maxwell equation. In the “infinity-ion-mass” limit, the unipolar Euler–Maxwell equation arises from the bipolar Euler–Maxwell equation, describing a coupled system for a plasma of electrons and ions. The non-relativistic limit c → ∞ of the Euler–Maxwell equation is the repulsive Euler–Poisson equation with electric force. We propose that the Euler–Poisswell equation, where the Euler equation with electric force is coupled to the magnetostatic O ( 1 / c ) approximation of Maxwell’s equations, is the correct semi-relativistic O ( 1 / c ) approximation of the Euler–Maxwell equation. In the Euler–Poisswell equation the fluid dynamics are decoupled from the magnetic field since the Lorentz force reduces to the electric force. The first non-trivial interaction with the magnetic field is at the O ( 1 / c 2 ) level in the Euler–Darwin equation. This is a consistent and self-consistent model of order O ( 1 / c 2 ) and includes the full Lorentz force, which is relativistic at O ( 1 / c 2 ). The Euler–Poisswell equation also arises as the semiclassical limit of the quantum Pauli–Poisswell equation, which is the O ( 1 / c ) approximation of the relativistic Dirac–Maxwell equation. We also present a local wellposedness theory for the Euler–Poisswell equation. The Euler–Maxwell system couples the non-relativistic Euler equation and the relativistic Maxwell equations and thus it is not fully consistent in 1 / c. The consistent fully relativistic model is the relativistic Euler–Maxwell equation where Maxwell’s equations are coupled to the relativistic Euler equation – a model that is neglected in the mathematics community. We also present the relativistic Euler–Darwin equation resulting as a O ( 1 / c 2 ) approximation of this model.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135088512","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
Comparison results for a nonlocal singular elliptic problem 一类非局部奇异椭圆问题的比较结果
4区 数学
Asymptotic Analysis Pub Date : 2023-11-10 DOI: 10.3233/asy-231860
Barbara Brandolini, Ida de Bonis, Vincenzo Ferone, Bruno Volzone
{"title":"Comparison results for a nonlocal singular elliptic problem","authors":"Barbara Brandolini, Ida de Bonis, Vincenzo Ferone, Bruno Volzone","doi":"10.3233/asy-231860","DOIUrl":"https://doi.org/10.3233/asy-231860","url":null,"abstract":"We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are presented, depending on the summability of the right-hand side of the equation. The maximum principle arguments employed in the core of the proofs of the main results offer a nonstandard, flexible alternative to the ones described in (Arch. Ration. Mech. Anal. 239 (2021) 1733–1770, Theorem 31). Some interesting consequences are L p regularity results and nonlocal energy estimates for solutions.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087589","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
Some remarks on simplified double porosity model of immiscible incompressible two-phase flow 非混相不可压缩两相流简化双孔隙率模型的几点思考
4区 数学
Asymptotic Analysis Pub Date : 2023-11-10 DOI: 10.3233/asy-231866
M. Jurak, L. Pankratov, A. Vrbaški
{"title":"Some remarks on simplified double porosity model of immiscible incompressible two-phase flow","authors":"M. Jurak, L. Pankratov, A. Vrbaški","doi":"10.3233/asy-231866","DOIUrl":"https://doi.org/10.3233/asy-231866","url":null,"abstract":"The paper is devoted to the derivation, by linearization, of simplified homogenized models of an immiscible incompressible two-phase flow in double porosity media in the case of thin fissures. In a simplified double porosity model derived previously by the authors the matrix-fracture source term is approximated by a convolution type source term. This approach enables to exclude the cell problem, in form of the imbibition equation, from the global double porosity model. In this paper we propose a new linear version of the imbibition equation which leads to a new simplified double porosity model. We also present numerical simulations which show that the matrix-fracture exchange term based on this new linearization procedure gives a better approximation of the exact one than the corresponding exchange term obtained earlier by the authors.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135088347","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
Global existence and asymptotic behaviour for a viscoelastic plate equation with nonlinear damping and logarithmic nonlinearity 具有非线性阻尼和对数非线性的粘弹性板方程的全局存在性和渐近性态
4区 数学
Asymptotic Analysis Pub Date : 2023-11-10 DOI: 10.3233/asy-231859
Bhargav Kumar Kakumani, Suman Prabha Yadav
{"title":"Global existence and asymptotic behaviour for a viscoelastic plate equation with nonlinear damping and logarithmic nonlinearity","authors":"Bhargav Kumar Kakumani, Suman Prabha Yadav","doi":"10.3233/asy-231859","DOIUrl":"https://doi.org/10.3233/asy-231859","url":null,"abstract":"In this article, we consider a viscoelastic plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping term. Here we prove the existence of the solution to the problem using the Faedo–Galerkin method. Also, we prove few general decay rate results.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087591","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
On periodic and compactly supported least energy solutions to semilinear elliptic equations with non-Lipschitz nonlinearity 非lipschitz非线性半线性椭圆方程的周期紧支最小能量解
4区 数学
Asymptotic Analysis Pub Date : 2023-11-10 DOI: 10.3233/asy-231878
Jacques Giacomoni, Yavdat Il’yasov, Deepak Kumar
{"title":"On periodic and compactly supported least energy solutions to semilinear elliptic equations with non-Lipschitz nonlinearity","authors":"Jacques Giacomoni, Yavdat Il’yasov, Deepak Kumar","doi":"10.3233/asy-231878","DOIUrl":"https://doi.org/10.3233/asy-231878","url":null,"abstract":"We discuss the existence and non-existence of periodic in one variable and compactly supported in the other variables least energy solutions for equations with non-Lipschitz nonlinearity of the form: − Δ u = λ u p − u q in R N + 1 , where 0 < q < p < 1 and λ ∈ R. The approach is based on the Nehari manifold method supplemented by a one-sided constraint given through the functional of the suitable Pohozaev identity. The limit value of the parameter λ, where the approach is applicable, corresponds to the existence of periodic in one variable and compactly supported in the other variables least energy solutions. This value is found through the extrem values of nonlinear generalized Rayleigh quotients and the so-called curve of the critical exponents of p, q. Important properties of the solutions are derived for suitable ranges of the parameters, such as that they are not trivial with respect to the periodic variable and do not coincide with compactly supported solutions on the entire space R N + 1 .","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135137214","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
Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: Strong boundary interactions 类图网络中对流占优输运问题的Puiseux渐近展开:强边界相互作用
4区 数学
Asymptotic Analysis Pub Date : 2023-11-10 DOI: 10.3233/asy-231876
Taras Mel’nyk, Christian Rohde
{"title":"Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: Strong boundary interactions","authors":"Taras Mel’nyk, Christian Rohde","doi":"10.3233/asy-231876","DOIUrl":"https://doi.org/10.3233/asy-231876","url":null,"abstract":"This article completes the study of the influence of the intensity parameter α in the boundary condition ε ∂ ν ε u ε − u ε V ε → · ν ε = ε α φ ε given on the boundary of a thin three-dimensional graph-like network consisting of thin cylinders that are interconnected by small domains (nodes) with diameters of order O ( ε ). Inside of the thin network a time-dependent convection-diffusion equation with high Péclet number of order O ( ε − 1 ) is considered. The novelty of this article is the case of α < 1, which indicates a strong intensity of physical processes on the boundary, described by the inhomogeneity φ ε (the cases α = 1 and α > 1 were previously studied by the same authors). A complete Puiseux asymptotic expansion is constructed for the solution u ε as ε → 0, i.e., when the diffusion coefficients are eliminated and the thin network shrinks into a graph. Furthermore, the corresponding uniform pointwise and energy estimates are proved, which provide an approximation of the solution with a given accuracy in terms of the parameter ε.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135137224","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
Fractional diffusion for Fokker–Planck equation with heavy tail equilibrium: An à la Koch spectral method in any dimension 具有重尾平衡的Fokker-Planck方程的分数扩散:任意维的<s:1> la Koch谱方法
4区 数学
Asymptotic Analysis Pub Date : 2023-10-24 DOI: 10.3233/asy-231870
Dahmane Dechicha, Marjolaine Puel
{"title":"Fractional diffusion for Fokker–Planck equation with heavy tail equilibrium: An à la Koch spectral method in any dimension","authors":"Dahmane Dechicha, Marjolaine Puel","doi":"10.3233/asy-231870","DOIUrl":"https://doi.org/10.3233/asy-231870","url":null,"abstract":"In this paper, we extend the spectral method developed (Dechicha and Puel (2023)) to any dimension d ⩾ 1, in order to construct an eigen-solution for the Fokker–Planck operator with heavy tail equilibria, of the form ( 1 + | v | 2 ) − β 2 , in the range β ∈ ] d , d + 4 [. The method developed in dimension 1 was inspired by the work of H. Koch on nonlinear KdV equation (Nonlinearity 28 (2015) 545). The strategy in this paper is the same as in dimension 1 but the tools are different, since dimension 1 was based on ODE methods. As a direct consequence of our construction, we obtain the fractional diffusion limit for the kinetic Fokker–Planck equation, for the correct density ρ : = ∫ R d f d v, with a fractional Laplacian κ ( − Δ ) β − d + 2 6 and a positive diffusion coefficient κ.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135316388","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
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