A reaction-diffusion model for a class of nonlinear parabolic equations with moving boundaries: Existence, uniqueness, exponential decay and simulation

• Tipo: Artigo em Revista Científica Internacional
• Data: 2014

Autores

Maria do Carmo Coimbra (Autor) FEUP

Revista

Título: Applied Mathematical Modelling

Vol. 38

Páginas: 5609-5622

ISSN: 0307-904X

Editora: Elsevier

Indexação

ISI Web of Knowledge - 8 Citações

ISI Web of Science

Scopus - 8 Citações

COMPENDEX

Current Contents

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

CORDIS: Ciências Físicas > Matemática > Matemática aplicada > Análise numérica

Outras Informações

ID Authenticus: P-00A-1QG

DOI: 10.1016/j.apm.2014.04.045

Abstract (EN): The aim of this paper is to establish the existence, uniqueness and asymptotic behaviour of a strong regular solution for a class of nonlinear equations of reaction-diffusion nonlocal type with moving boundaries: {u(t) - a (integral(Omega t) u(x, t)dx)u(xx) = f (x, t), (x, t) is an element of Q(t), u(alpha(t), t) = u(beta(t), t) = 0, t > 0, u(x, 0) = u(0)(x), x is an element of Omega(0) =]alpha(0),beta(0)[, where Q(t) is a bounded non-cylindrical domain defined by Q(t) = {(x, t) is an element of R-2 : alpha(t) < x < beta(t), for all 0 < t < T}. Moreover, we study the properties of the solution and implement a numerical algorithm based on the Moving Finite Element Method (MFEM) with polynomial approximations of any degree, to solve this class of problems. Some numerical tests are investigated to evaluate the performance of our Matlab code based on the MFEM and illustrate the exponential decay of the solution.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 14