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On the initial growth of interfaces in reaction-diffusion equations with strong absorption

Díaz Díaz, Jesús Ildefonso and Álvarez León, Luis (1993) On the initial growth of interfaces in reaction-diffusion equations with strong absorption. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 123 (5). pp. 803-817. ISSN 0308-2105

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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.


Item Type:Article
Uncontrolled Keywords:heat-equation; thermal waves; media
Subjects:Sciences > Mathematics > Differential equations
ID Code:16257
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