Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed

Marek Fila; Michael Winkler

doi:10.4171/jems/105

JournalsjemsVol. 10, No. 1pp. 105–132

Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed

Marek Fila
Comenius University, Bratislava, Slovak Republic
Michael Winkler
Universität Paderborn, Germany

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Abstract

We consider a reaction-diffusion-convection equation on the halfline $(0, \infty)$ with the zero Dirichlet boundary condition at $x = 0$ . We find a positive selfsimilar solution $u$ which blows up in a finite time $T$ at $x = 0$ while $u (x, T)$ remains bounded for $x > 0$ .

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Marek Fila, Michael Winkler, Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed. J. Eur. Math. Soc. 10 (2008), no. 1, pp. 105–132

DOI 10.4171/JEMS/105