On Spike Solutions of Singularly Perturbed Semilinear Dirichlet Problem
نویسندگان
چکیده
منابع مشابه
Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem
A semilinear reaction-diffusion two-point boundary value problem, whose secondorder derivative is multiplied by a small positive parameter ε2, is considered. It can have multiple solutions. The numerical computation of solutions having interior transition layers is analysed. It is demonstrated that the accurate computation of such solutions is exceptionally difficult. To address this difficulty...
متن کاملThe Dirichlet Problem for Singularly Perturbed Elliptic Equations
There has been much work on various singularly perturbed partial differential equations or systems. Such equations or systems depend on some small parameters ε > 0, solutions denoted as uε. There are at least two types of questions being investigated. The first type is to study possible behavior of uε as ε tends to zero. The second is to actually construct, by various methods, such solutions. I...
متن کاملA uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions
This paper considers a simple central difference scheme for a singularly perturbed semilinear reaction–diffusion problem, which may have multiple solutions. Asymptotic properties of solutions to this problem are discussed and analyzed. To compute accurate approximations to these solutions, we consider a piecewise equidistant mesh of Shishkin type, which contains O(N) points. On such a mesh, we ...
متن کاملOn Finding Multiple Solutions to a Singularly Perturbed Neumann Problem
In this paper, in order to numerically solve for multiple positive solutions to a singularly perturbed Neumann boundary value problem in mathematical biology and other applications, a local minimax method is modified with new local mesh refinement and other strategies. Algorithm convergence and other related properties are verified. Motivated by the numerical algorithm and convinced by the nume...
متن کاملMultipeak Solutions for a Singularly Perturbed Neumann Problem
Problem (1.1) appears in applied mathematics. See for example [13, 14] and the references therein. For the interesting link between this problem and the modelling of activator-inhibitor systems, the authors can refer to [11]. In [13, 14], Ni and Takagi prove that the least energy solution of (1.1) has exactly one local maximum point xε which lies in ∂Ω, and xε tends to a point x0 which attains ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1994
ISSN: 0022-0396
DOI: 10.1006/jdeq.1994.1154