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Some Results on Blow up for Semilinear Parabolic Problems

Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 47)

Abstract

We discuss on recent results concerning the asymptotics near blow-up of nonnega-tive solutions of
$$\begin{array}{*{20}{c}} {{{u}_{t}} = {{u}_{{xx}}} + f\left( u \right); - \infty < x < \infty ,t > 0} \hfill \\ {u\left( {x,0} \right) = {{u}_{0}}\left( x \right); - \infty < x < \infty ,} \hfill \\ \end{array}$$
where f (u)=u p with p > 1 or f (u) = eu, and u 0(x) is continuous, nonnegative and bounded. AMS(MOS) subject classifications. 35B40, 35K55, 35K57

Key words and phrases

Semilinear parabolic problems blow up asymptotic behaviour of solutions 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  1. 1.Departamento de Matematica AplicadaUniversidad Complutense, Facultad de MatematicasMadridSpain
  2. 2.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA

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