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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The blow-up boundary for nonlinear wave equations
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by Luis A. Caffarelli and Avner Friedman PDF
Trans. Amer. Math. Soc. 297 (1986), 223-241 Request permission

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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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 297 (1986), 223-241
  • MSC: Primary 35L70
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0849476-3
  • MathSciNet review: 849476