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
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