We consider a reaction-diffusion-convection equation on the halfline with the zero Dirichlet boundary condition at . We find a positive selfsimilar solution which blows up in a finite time at while remains bounded for .
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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