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Homogenization of a class of singular elliptic problems in two-component domains 双分量域上一类奇异椭圆型问题的均匀化
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-06-06 DOI: 10.3233/asy-221783
F. Raimondi
{"title":"Homogenization of a class of singular elliptic problems in two-component domains","authors":"F. Raimondi","doi":"10.3233/asy-221783","DOIUrl":"https://doi.org/10.3233/asy-221783","url":null,"abstract":"This paper deals with the homogenization of a quasilinear elliptic problem having a singular lower order term and posed in a two-component domain with an ε-periodic imperfect interface. We prescribe a Dirichlet condition on the exterior boundary, while we assume that the continuous heat flux is proportional to the jump of the solution on the interface via a function of order ε γ . We prove an homogenization result for − 1 < γ < 1 by means of the periodic unfolding method (see SIAM J. Math. Anal. 40 (2008) 1585–1620 and The Periodic Unfolding Method (2018) Springer), adapted to two-component domains in (J. Math. Sci. 176 (2011) 891–927). One of the main tools in the homogenization process is a convergence result for a suitable auxiliary linear problem, associated with the weak limit of the sequence { u ε } of the solutions, as ε → 0. More precisely, our result shows that the gradient of u ε behaves like that of the solution of the auxiliary problem, which allows us to pass to the limit in the quasilinear term, and to study the singular term near its singularity, via an accurate a priori estimate.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47998750","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
Upper semicontinuity of pullback attractors for nonclassical diffusion equations with delay 非经典时滞扩散方程拉回吸引子的上半连续性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-06-06 DOI: 10.3233/asy-221782
Yuming Qin, Qitao Cai
{"title":"Upper semicontinuity of pullback attractors for nonclassical diffusion equations with delay","authors":"Yuming Qin, Qitao Cai","doi":"10.3233/asy-221782","DOIUrl":"https://doi.org/10.3233/asy-221782","url":null,"abstract":"In this paper, we mainly study the upper semicontinuity of pullback D-attractors for a nonclassical diffusion equation with delay term b ( t , u t ) which contains some hereditary characteristics. Under a critical nonlinearity f, a time-dependent force g ( t , x ) with exponential growth and a delayed force term b ( t , u t ), using the asymptotic a priori estimate method, we prove the upper semicontinuity of pullback D-attractor { A ε ( t ) } t ∈ R to equation (1.1) with ε ∈ [ 0 , 1 ].","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42654632","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 nonlinear Dirichlet problem involving terms with logarithmic growth 一个包含对数增长项的非线性Dirichlet问题
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-05-06 DOI: 10.3233/asy-221773
Andrea Polito
{"title":"A nonlinear Dirichlet problem involving terms with logarithmic growth","authors":"Andrea Polito","doi":"10.3233/asy-221773","DOIUrl":"https://doi.org/10.3233/asy-221773","url":null,"abstract":"We study existence and regularity of weak solutions for a class of boundary value problems, whose form is − div ( log ( 1 + | ∇ u | ) | ∇ u | m ( x ) ∇ u ) + u | ∇ u | log ( 1 + | ∇ u | ) = f ( x ) , in  Ω u = 0 , on  ∂ Ω where both the principal part and the lower order term have a logarithmic growth with respect to the gradient of the solutions. We prove that the solutions, due to the regularizing effect given by the lower order term, belong to the Orlicz–Sobolev space generated by the function s log ( 1 + | s | ) even for L 1 ( Ω ) data.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45612854","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
Stochastic homogenization of nonconvex integrals in the space of functions of bounded deformation 有界变形函数空间中非凸积分的随机均匀化
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-05-06 DOI: 10.3233/asy-221772
Omar Anza Hafsa, Jean-Philippe Mandallena
{"title":"Stochastic homogenization of nonconvex integrals in the space of functions of bounded deformation","authors":"Omar Anza Hafsa, Jean-Philippe Mandallena","doi":"10.3233/asy-221772","DOIUrl":"https://doi.org/10.3233/asy-221772","url":null,"abstract":"We study stochastic homogenization by Γ-convergence of nonconvex integrals of the calculus of variations in the space of functions of bounded deformation.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":"209 ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41310222","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
Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result 标量值和矢量值Allen–Cahn方程对高维90°接触角平均曲率流的收敛性，第一部分：收敛结果
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-05-06 DOI: 10.3233/asy-221775
Maximilian Moser
{"title":"Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result","authors":"Maximilian Moser","doi":"10.3233/asy-221775","DOIUrl":"https://doi.org/10.3233/asy-221775","url":null,"abstract":"We consider the sharp interface limit for the scalar-valued and vector-valued Allen–Cahn equation with homogeneous Neumann boundary condition in a bounded smooth domain Ω of arbitrary dimension N ⩾ 2 in the situation when a two-phase diffuse interface has developed and intersects the boundary ∂ Ω. The limit problem is mean curvature flow with 90°-contact angle and we show convergence in strong norms for well-prepared initial data as long as a smooth solution to the limit problem exists. To this end we assume that the limit problem has a smooth solution on [ 0 , T ] for some time T > 0. Based on the latter we construct suitable curvilinear coordinates and set up an asymptotic expansion for the scalar-valued and the vector-valued Allen–Cahn equation. In order to estimate the difference of the exact and approximate solutions with a Gronwall-type argument, a spectral estimate for the linearized Allen–Cahn operator in both cases is required. The latter will be shown in a separate paper, cf. (Moser (2021)).","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41322933","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: 5
Nonlocal p-Kirchhoff equations with singular and critical nonlinearity terms 具有奇异和临界非线性项的非局部p-Kirchhoff方程
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-05-03 DOI: 10.3233/ASY-221769
A. Ghanmi, M. Kratou, K. Saoudi, Dušan D. Repovš
{"title":"Nonlocal p-Kirchhoff equations with singular and critical nonlinearity terms","authors":"A. Ghanmi, M. Kratou, K. Saoudi, Dušan D. Repovš","doi":"10.3233/ASY-221769","DOIUrl":"https://doi.org/10.3233/ASY-221769","url":null,"abstract":"The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities: ( [ u ] s , p p ) σ − 1 ( − Δ ) p s u = λ u γ + u p s ∗ − 1 in  Ω , u > 0 , in  Ω , u = 0 , in  R N ∖ Ω , where Ω is a bounded domain in R N with the smooth boundary ∂ Ω, 0 < s < 1 < p < ∞, N > s p, 1 < σ < p s ∗ / p, with p s ∗ = N p N − p s , ( − Δ ) p s is the nonlocal p-Laplace operator and [ u ] s , p is the Gagliardo p-seminorm. We combine some variational techniques with a truncation argument in order to show the existence and the multiplicity of positive solutions to the above problem.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46123634","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
Asymptotic of the dissipative eigenvalues of Maxwell’s equations Maxwell方程耗散特征值的渐近性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-04-25 DOI: 10.3233/asy-231837
V. Petkov
{"title":"Asymptotic of the dissipative eigenvalues of Maxwell’s equations","authors":"V. Petkov","doi":"10.3233/asy-231837","DOIUrl":"https://doi.org/10.3233/asy-231837","url":null,"abstract":"Let Ω = R 3 ∖ K ¯, where K is an open bounded domain with smooth boundary Γ. Let V ( t ) = e t G b , t ⩾ 0, be the semigroup related to Maxwell’s equations in Ω with dissipative boundary condition ν ∧ ( ν ∧ E ) + γ ( x ) ( ν ∧ H ) = 0, γ ( x ) > 0, ∀ x ∈ Γ. We study the case when γ ( x ) ≠ 1, ∀ x ∈ Γ, and we establish a Weyl formula for the counting function of the eigenvalues of G b in a polynomial neighbourhood of the negative real axis.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41905955","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
Smooth dynamics of a Timoshenko system with hybrid dissipation 具有混合耗散的Timoshenko系统的光滑动力学
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-04-14 DOI: 10.3233/asy-221768
Yuming Qin, Jaime E. Muñoz Rivera, T. Ma
{"title":"Smooth dynamics of a Timoshenko system with hybrid dissipation","authors":"Yuming Qin, Jaime E. Muñoz Rivera, T. Ma","doi":"10.3233/asy-221768","DOIUrl":"https://doi.org/10.3233/asy-221768","url":null,"abstract":"In this paper we study the longtime dynamics of a class of thermoelastic Timoshenko beams with history in a nonlinear elastic foundation. Our main result establishes the existence of a global attractor with finite fractal dimension without requiring the so-called equal wave speeds assumption. In addition, the attractor belongs to the phase space of strong solutions. The results are based on properties of gradient systems and a concept of quasi-stability. We believe this is the first study on the existence of global attractors for semilinear Timoshenko systems with hybrid dissipation (heat and memory).","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42739307","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
Gevrey regularity and summability of the formal power series solutions of the inhomogeneous generalized Boussinesq equations 非齐次广义Boussinesq方程形式幂级数解的Gevrey正则性和可和性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-03-23 DOI: 10.3233/asy-221764
Pascal Remy
{"title":"Gevrey regularity and summability of the formal power series solutions of the inhomogeneous generalized Boussinesq equations","authors":"Pascal Remy","doi":"10.3233/asy-221764","DOIUrl":"https://doi.org/10.3233/asy-221764","url":null,"abstract":"In this article, we investigate Gevrey and summability properties of the formal power series solutions of the inhomogeneous generalized Boussinesq equations. Even if the case that really matters physically is an analytic inhomogeneity, we systematically examine here the cases where the inhomogeneity is s-Gevrey for any s ⩾ 0, in order to carefully distinguish the influence of the data (and their degree of regularity) from that of the equation (and its structure). We thus prove that we have a noteworthy dichotomy: for any s ⩾ 1, the formal solutions and the inhomogeneity are simultaneously s-Gevrey; for any s < 1, the formal solutions are generically 1-Gevrey. In the latter case, we give in particular an explicit example in which the formal solution is s ′ -Gevrey for no s ′ < 1, that is exactly 1-Gevrey. Then, we give a necessary and sufficient condition under which the formal solutions are 1-summable in a given direction arg ( t ) = θ. In addition, we present some technical results on the generalized binomial and multinomial coefficients, which are needed for the proofs of our various results.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42403739","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
Diffusion–reaction–dissolution–precipitation model in a heterogeneous porous medium with nonidentical diffusion coefficients: Analysis and homogenization 具有不同扩散系数的非均质多孔介质中的扩散-反应-溶解-沉淀模型:分析和均质化
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-03-14 DOI: 10.3233/asy-221763
Nibedita Ghosh, H. Mahato
{"title":"Diffusion–reaction–dissolution–precipitation model in a heterogeneous porous medium with nonidentical diffusion coefficients: Analysis and homogenization","authors":"Nibedita Ghosh, H. Mahato","doi":"10.3233/asy-221763","DOIUrl":"https://doi.org/10.3233/asy-221763","url":null,"abstract":"We study a pore-scale model where two mobile species with different diffusion coefficients react and precipitate in the form of immobile species (crystal) on the surface of the solid parts in a porous medium. The reverse may also happen, i.e. the crystals may dissolute to give mobile species. The mathematical modeling of these processes will give rise to a coupled system of ordinary and partial differential equations. We first prove the existence of a unique nonnegative global weak solution and then upscale the model from microscale to macroscale.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48202142","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: 3
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