Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/46214
Title: On the initial growth of interfaces in reaction-diffusion equations with strong absorption
Authors: Alvarez, Luis 
Diaz, Jesus Ildefonso
UNESCO Clasification: 1206 Análisis numérico
120601 Construcción de algoritmos
120602 Ecuaciones diferenciales
Keywords: Heat-Equation
Thermal Waves
Media
Issue Date: 1993
Journal: Proceedings of the Royal Society of Edinburgh Section A: Mathematics 
Abstract: We study the initial growth of the interfaces of non-negative local solutions of the equation u(t) = (u(m))xx - lambdau(q) when m greater-than-or-equal-to 1 and 0 < q < 1. We show that if u(x, 0) greater-than-or-equal-to C(-x)+2/(m-q) with C > C0, for some explicit C0 = C0(lambda, m, q), then the free boundary zeta(t) = sup {x: u(x, t) > 0} is a ''heating front''. More precisely zeta(t) greater-than-or-equal-to at(m-q)/2(1-q) for any t small enough and for some a > 0. If on the contrary, u(x, 0) less-than-or-equal-to C(-x)+2/(m-q) with C < C0, then zeta(t) is a ''cooling front'' and in fact zeta(t) less-than-or-equal-to -at(m-q)/2(1-q) for any t small enough and for some a > 0. Applications to solutions of the associated Cauchy and Dirichlet problems are also given.
URI: http://hdl.handle.net/10553/46214
ISSN: 0308-2105
DOI: 10.1017/S0308210500029504
Source: Proceedings of the Royal Society of Edinburgh: Section A Mathematics [ISSN 0308-2105], v.123 (5), p. 803-817
Appears in Collections:Artículos
Show full item record

SCOPUSTM   
Citations

8
checked on Jul 17, 2022

WEB OF SCIENCETM
Citations

6
checked on Feb 25, 2024

Page view(s)

89
checked on Dec 16, 2023

Google ScholarTM

Check

Altmetric


Share



Export metadata



Items in accedaCRIS are protected by copyright, with all rights reserved, unless otherwise indicated.