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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Abdulla, Ugur G. 2002. Evolution of interfaces and explicit asymptotics at infinity for the fast diffusion equation with absorption. Nonlinear Analysis: Theory, Methods & Applications, Vol. 50, Issue. 4, p. 541.

    Abdulla, Ugur G. and King, John R. 2000. Interface Development and Local Solutions to Reaction-Diffusion Equations. SIAM Journal on Mathematical Analysis, Vol. 32, Issue. 2, p. 235.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 123, Issue 5
  • January 1993, pp. 803-817

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

  • Luis Alvarez (a1) and Jesus Ildefonso Diaz (a2)
  • DOI:
  • Published online: 14 November 2011

We study the initial growth of the interfaces of non-negative local solutions of the equation ut = (um)xx−λuq when m ≧ 1 and 0<q <1. We show that if with C < C0, for some explicit C0 = C0(λ, m, q), then the free boundary Ϛ(t) = sup {x:u(x, t) > 0} is a ‘heating front’. More precisely Ϛ(t) ≧at(m−q)/2(1−q) for any t small enough and for some a>0. If on the contrary, with C<C0, then Ϛ(t) is a ‘cooling front’ and in fact Ϛ(t) ≧ −atm−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.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
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