Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The blow-up boundary for nonlinear wave equations

Authors: Luis A. Caffarelli and Avner Friedman
Journal: Trans. Amer. Math. Soc. 297 (1986), 223-241
MSC: Primary 35L70
MathSciNet review: 849476
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Abstract: Consider the Cauchy problem for a nonlinear wave equation $ \square u = F(u)$ in $ N$ space dimensions, $ N \leqslant 3$, with $ F$ superlinear and nonnegative. It is well known that, in general, the solution blows up in finite time. In this paper it is shown, under some assumptions on the Cauchy data, that the blow-up set is a space-like surface $ t = \phi (x)$ with $ \phi (x)$ continuously differentiable.

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Article copyright: © Copyright 1986 American Mathematical Society