ArticleOriginal scientific text

Title

Nonlinear Heat Equation with a Fractional Laplacian in a Disk

Authors 1

Affiliations

  1. Departamento de Matemáticas, Escuela Colombiana de Ingeniería, A.A. 14520, Bogotá, Colombia

Abstract

For the nonlinear heat equation with a fractional Laplacian ut+(-Δ)α2u=u2, 1 < α ≤ 2, the first initial-boundary value problem in a disk is considered. Small initial conditions, homogeneous boundary conditions, and periodicity conditions in the angular coordinate are imposed. Existence and uniqueness of a global-in-time solution is proved, and the solution is constructed in the form of a series of eigenfunctions of the Laplace operator in the disk. First-order long-time asymptotics of the solution is obtained.

Keywords

nonlinear heat equation, long-time asymptotics, fractional Laplacian, initial-boundary value problem in a disk

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Pages:
101-122
Main language of publication
English
Received
1998-11-06
Accepted
1999-02-01
Published
1999
Exact and natural sciences