On the initial growth of interfaces in reaction–diffusion equations with strong absorption
Luis Álvarez, Jesús Ildefonso Díaz Díaz · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1993
We study the initial growth of the interfaces of non-negative local solutions of the equation u t = (u m ) xx −λu q when m ≧ 1 and 0 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 0 , then Ϛ( t ) is a ‘cooling front’ and in fact Ϛ( t ) ≧ − 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.