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The blow-up curve of solutions of mixed problems for semilinear wave equations with exponential nonlinearities in one space dimension, I

par Godin, Paul
Référence Calculus of variations and partial differential equations, 13, 1, page (69-95)
Publication Publié, 2001-08

Article révisé par les pairs

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Résumé :

In this paper, we consider mixed problems with a spacelike boundary derivative condition for semilinear wave equations with exponential nonlinearities in a quarter plane. Results similar to those obtained earlier by Caffarelli-Friedman for Cauchy problems and power nonlinearities are proved in the present situation, namely we show that solutions either are global or blow up on a C1 spacelike curve. Weaker results are also obtained if the boundary vector field is tangent to the characteristic which leaves the domain in the future.