Asymptotic Analysis最新文献

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Divergent sequence of nontrivial solutions for superlinear double phase problems 超线性双相问题非平凡解的发散序列
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-03-06 DOI: 10.3233/asy-231830
Nikolaos S. Papageorgiou, C. Vetro, F. Vetro
{"title":"Divergent sequence of nontrivial solutions for superlinear double phase problems","authors":"Nikolaos S. Papageorgiou, C. Vetro, F. Vetro","doi":"10.3233/asy-231830","DOIUrl":"https://doi.org/10.3233/asy-231830","url":null,"abstract":"We consider a double phase (unbalanced growth) Dirichlet problem with a Carathéodory reaction f ( z , x ) which is superlinear in x but without satisfying the AR-condition. Using the symmetric mountain pass theorem, we produce a whole sequence of distinct bounded solutions which diverge to infinity.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43753457","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 solutions to coupled (Navier-)Stokes Newton systems in R 3 三维耦合(Navier-)Stokes - Newton系统的全局解
4区 数学
Asymptotic Analysis Pub Date : 2023-03-02 DOI: 10.3233/asy-221790
M. Hillairet, L. Sabbagh
{"title":"Global solutions to coupled (Navier-)Stokes Newton systems in R 3","authors":"M. Hillairet, L. Sabbagh","doi":"10.3233/asy-221790","DOIUrl":"https://doi.org/10.3233/asy-221790","url":null,"abstract":"We consider the motion of spherical particles in the whole space R 3 filled with a viscous fluid. We show that, when modelling the fluid behavior with an incompressible Stokes system, solutions are global and no collision occurs between the spheres in finite time.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135383663","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
Boundary localization of transmission eigenfunctions in spherically stratified media 球面分层介质中传输特征函数的边界定位
4区 数学
Asymptotic Analysis Pub Date : 2023-03-02 DOI: 10.3233/asy-221794
Jiang, Yan, Liu, Hongyu, Zhang, Jiachuan, Zhang, Kai
{"title":"Boundary localization of transmission eigenfunctions in spherically stratified media","authors":"Jiang, Yan, Liu, Hongyu, Zhang, Jiachuan, Zhang, Kai","doi":"10.3233/asy-221794","DOIUrl":"https://doi.org/10.3233/asy-221794","url":null,"abstract":"Consider the transmission eigenvalue problem for u ∈ H 1 ( Ω ) and v ∈ H 1 ( Ω ): ∇ · ( σ ∇ u ) + k 2 n 2 u = 0 in Ω , Δ v + k 2 v = 0 in Ω , u = v , σ ∂ u ∂ ν = ∂ v ∂ ν on ∂ Ω , where Ω is a ball in R N , N = 2 , 3. If σ and n are both radially symmetric, namely they are functions of the radial parameter r only, we show that there exists a sequence of transmission eigenfunctions { u m , v m } m ∈ N associated with k m → + ∞ as m → + ∞ such that the L 2 -energies of v m ’s are concentrated around ∂ Ω. If σ and n are both constant, we show the existence of transmission eigenfunctions { u j , v j } j ∈ N such that both u j and v j are localized around ∂ Ω. Our results extend the recent studies in (SIAM J. Imaging Sci. 14 (2021), 946–975; Chow et al.). Through numerics, we also discuss the effects of the medium parameters, namely σ and n, on the geometric patterns of the transmission eigenfunctions.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135383283","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
Singularity extraction for elliptic equations with coefficients with jumps and Dirac sources 带跳跃和Dirac源的系数椭圆型方程的奇异性提取
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-02-13 DOI: 10.3233/asy-221824
Eya Bejaoui, F. Ben Belgacem
{"title":"Singularity extraction for elliptic equations with coefficients with jumps and Dirac sources","authors":"Eya Bejaoui, F. Ben Belgacem","doi":"10.3233/asy-221824","DOIUrl":"https://doi.org/10.3233/asy-221824","url":null,"abstract":"We explore the mathematical structure of the solution to an elliptic diffusion problem with point-wise Dirac sources. The conductivity parameter is space-varying, may have jumps and the Dirac sources may be located along the discontinuity curves of that parameter. The variational problem, issued by duality, is proven to be well posed using a sharp elliptic regularity result by Di-Giorgi [Mem. Accad. Sci. Torino, 3, 1957]. The paper is aimed at a key expansion into a split singular/regular contributions. The singular part is calculated by an explicit formula, while the regular correction can be computed as the solution to a standard variational Poisson problem. The latter can be successfully approximated by most of the numerical methods practiced nowadays. Some analytical examples are discussed at last to assess the minimality of the assumptions we use to establish our theoretical results.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42309073","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 method and transient terms in exact controls 精确控制的渐近方法和暂态项
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-02-08 DOI: 10.3233/asy-231829
P. Destuynder
{"title":"Asymptotic method and transient terms in exact controls","authors":"P. Destuynder","doi":"10.3233/asy-231829","DOIUrl":"https://doi.org/10.3233/asy-231829","url":null,"abstract":"There is a narrow but hidden link between optimal control theory and the so-called Tikhonov regularization method. In fact, the small coefficient representing the marginal cost of the control can be interpreted as the regularization parameter in a Tikhonov method as far as there exists an exact control. This strategy enables one to adjust the cost function in the optimal control model in order to define the exact control which minimizes a given functional involving both the control but also the state variables during the control process. The goal of this paper is to suggest a method which gives a simple way to characterize and compute the exact control corresponding to the minimum of a given cost functional as said above. It appears as an extension of the phase control which is a finite dimensional version of the HUM control of J.L. Lions but for partial differential equations.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44561125","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 and multiplicity of multi-bump solutions for the double phase Kirchhoff problems with convolution term in R N rn中具有卷积项的双相Kirchhoff问题多凸解的存在性和多重性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-01-25 DOI: 10.3233/asy-231827
Shuaishuai Liang, S. Shi
{"title":"Existence and multiplicity of multi-bump solutions for the double phase Kirchhoff problems with convolution term in R N","authors":"Shuaishuai Liang, S. Shi","doi":"10.3233/asy-231827","DOIUrl":"https://doi.org/10.3233/asy-231827","url":null,"abstract":"In this paper, we study a class of the ( p , q ) Kirchhoff type problems with convolution term in R N . With the appropriate assumptions on potential function V and convolution term f, together with the penalization techniques, Morse iterative method and variational method, the existence and multiplicity of multi-bump solutions are obtained for this problem. In some sense, our results also generalize some known results.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42937661","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
Polynomial stabilization for thermoelastic Reissner–Mindlin–Timoshenko plates with structural damping 具有结构阻尼的热弹性Reissner–Mindlin–Timoshenko板的多项式镇定
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-01-23 DOI: 10.3233/asy-231826
A. Ramos, A. Araujo, A. Campelo, M. Freitas, L. S. Veras
{"title":"Polynomial stabilization for thermoelastic Reissner–Mindlin–Timoshenko plates with structural damping","authors":"A. Ramos, A. Araujo, A. Campelo, M. Freitas, L. S. Veras","doi":"10.3233/asy-231826","DOIUrl":"https://doi.org/10.3233/asy-231826","url":null,"abstract":"In this paper, we are interested in studying the well-posedness, optimal polynomial stability, and the lack of exponential stability for a class of thermoelastic system of Reissner–Mindlin–Timoshenko plates with structural damping, that is, with the dissipation of Kelvin–Voigt type on the equations for the rotation angles. We also consider the thermal effect with thermal variables described by Fourier’s law of heat conduction.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41340939","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
Optimal control of a model for brain lactate kinetics 脑乳酸动力学模型的最优控制
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-01-09 DOI: 10.3233/asy-221823
Hussein Raad, L. Cherfils, C. Allery, R. Guillevin
{"title":"Optimal control of a model for brain lactate kinetics","authors":"Hussein Raad, L. Cherfils, C. Allery, R. Guillevin","doi":"10.3233/asy-221823","DOIUrl":"https://doi.org/10.3233/asy-221823","url":null,"abstract":"The aim of this paper is to first study a Cahn-Hilliard model for brain lactate kinetics with a control function. This control allows for optimal treatment administered to ill patients suffering from glioma, in order to reduce their brain lactate concentrations, and thereby to slow down the tumor growth. We establish the well-posedness of the problem and the continuity of the control-to-state mapping, the existence of a minimizer of the objective functional, and its Fréchet differentiability in suitable Banach spaces with respect to the control and with respect to time. Moreover, we derive the first-order necessary conditions that an optimal control has to satisfy. In the second part of the paper, we illustrate our theoretical results with numerical simulations using MRI data from the University Hospital of Poitiers.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41880950","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
Cahn–Hilliard equation with regularization term 带正则化项的Cahn-Hilliard方程
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-01-03 DOI: 10.3233/asy-221821
Rim Mheich
{"title":"Cahn–Hilliard equation with regularization term","authors":"Rim Mheich","doi":"10.3233/asy-221821","DOIUrl":"https://doi.org/10.3233/asy-221821","url":null,"abstract":"We will study in this article the nonlinear Cahn–Hilliard equation with proliferation and regularization terms with regular and logarithmic potentials. First, we consider the regular potential case, we show that the solutions blow up in finite time or exist globally in time. Furthermore, we prove that the model possess a global attractor. In addition, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. In the second part, we consider the logarithmic potential case and show the existence of a global solution.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46091030","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 of nontrivial solution for quasilinear equations involving the 1-biharmonic operator 含1-二次谐波算子的拟线性方程非平凡解的存在性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-01-03 DOI: 10.3233/asy-221822
Huo Tao, Lin Li, Xiao-Qiong Yang
{"title":"Existence of nontrivial solution for quasilinear equations involving the 1-biharmonic operator","authors":"Huo Tao, Lin Li, Xiao-Qiong Yang","doi":"10.3233/asy-221822","DOIUrl":"https://doi.org/10.3233/asy-221822","url":null,"abstract":"In this paper, we study the existence results of a quasilinear elliptic problem involving the 1-biharmonic operator in R N , whose nonlinearity satisfies appropriate conditions. The existence theorem is proved through a new version of the Mountain Pass Theorem to locally Lipschitz functionals, where it is considered the Cerami compactness condition rather than the Palais–Smale one.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45847313","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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