Some asymptotic expansions for a semilinear reaction-diffusion problem in a sector

R. Bruce Kellogg; Natalia Kopteva

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arXiv · 0902.0987

Some asymptotic expansions for a semilinear reaction-diffusion problem in a sector

R. Bruce Kellogg·Natalia Kopteva

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Abstract

A semilinear singularly perturbed reaction-diffusion equation with Dirichlet boundary conditions is considered in a convex unbounded sector. The singular perturbation parameter is arbitrarily small, and the "reduced equation" may have multiple solutions. A formal asymptotic expansion for a possible solution is constructed that involves boundary and corner layer functions. For this asymptotic expansion, we establish certain inequalities that are used in a subsequent paper to construct sharp sub- and super-solutions and then establish the existence of a solution to a similar nonlinear elliptic problem in a convex polygon.

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R. Bruce Kellogg, Natalia Kopteva. 2009-09-27. Some asymptotic expansions for a semilinear reaction-diffusion problem in a sector. https://arxiv.org/abs/0902.0987

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