文献详情
Locator Function for Concentration Points in a Spatially Heterogeneous Semilinear Neumann Problem
文献类型：期刊
通讯作者：Takagi, I (reprint author), Renmin Univ China, Inst Math Sci, Beijing 100872, Peoples R China.; Takagi, I (reprint author), Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan.
期刊名称：INDIANA UNIVERSITY MATHEMATICS JOURNAL影响因子和分区
年：2019
卷：68
期：1
页码：63-103
ISSN：0022-2518
关键词：Concentration point; locator function; semilinear elliptic equation; anisotropic diffusion; spatial heterogeneity; ground-state solution; singular perturbation; pattern formation
所属部门：数学科学研究院
摘要：This paper is concerned with qualitative properties of solutions of the boundary value problem for a second-order semilinear elliptic equation with a small parameter in the coefficients of the highest-order differential operator. We study the asymptotic behavior of a family of solutions, called ground-state solutions, as the parameter approaches zero, in the case where all the coefficients depend on the spatial variable. We prove that a ground-state solution has only one local maximum, hence the ...More
This paper is concerned with qualitative properties of solutions of the boundary value problem for a second-order semilinear elliptic equation with a small parameter in the coefficients of the highest-order differential operator. We study the asymptotic behavior of a family of solutions, called ground-state solutions, as the parameter approaches zero, in the case where all the coefficients depend on the spatial variable. We prove that a ground-state solution has only one local maximum, hence the global maximum, and it is achieved at exactly one point. Moreover, the distribution of the ground-state solution is concentrated in a very narrow region around this unique maximum point. To locate the concentration point, we introduce the locator function defined by using the coefficients of the equation, and prove, for instance, that if the global minimum of the locator function over the domain is strictly smaller than a half of the minimum over the boundary, then the concentration point is in the interior of the domain and is in a small neighborhood of the global minimum point of the locator function. This shows a sharp contrast with the case of constant coefficients, where ground-state solutions are concentrated at a boundary point. ...Hide

DOI：10.1512/iumj.2019.68.7560
百度学术：Locator Function for Concentration Points in a Spatially Heterogeneous Semilinear Neumann Problem
语言：外文
基金：JSPS KAKENHIMinistry of Education, Culture, Sports, Science and Technology, Japan (MEXT)Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific Research (KAKENHI) [22244010, 26610027]
作者其他论文



STEADY STATES OF FITZHUGH-NAGUMO SYSTEM WITH NON-DIFFUSIVE ACTIVATOR AND DIFFUSIVE INHIBITOR.Li, Ying, Marciniak-Czochra, Anna, Takagi, Izumi, et al. .TOHOKU MATHEMATICAL JOURNAL. 2019, 71(2), 243-279.