# American Institute of Mathematical Sciences

August  2012, 5(4): 797-808. doi: 10.3934/dcdss.2012.5.797

## Stable and unstable initial configuration in the theory wave fronts

 1 University of Oklahoma, Noman, OK 73019, United States

Received  March 2011 Revised  May 2011 Published  November 2011

In this paper we study the wavefront like phase transition of solutions of a parabolic nonlinear boundary value problem used to model phase transitions in the theory of boiling liquids. Using weak supersolutions we provide bounds for the propagation speed of such a phase transition. Also we construct stable supersolutions to initial configurations which have locally supercritical values.
Citation: Ruediger Landes. Stable and unstable initial configuration in the theory wave fronts. Discrete & Continuous Dynamical Systems - S, 2012, 5 (4) : 797-808. doi: 10.3934/dcdss.2012.5.797
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