The blow-up surface for nonlinear wave equations with small spatial velocity
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- by Avner Friedman and Luc Oswald PDF
- Trans. Amer. Math. Soc. 308 (1988), 349-367 Request permission
Abstract:
Consider the Cauchy problem for ${u_{tt}} - {\varepsilon ^2}\Delta u = f(u)$ in space dimension $\leqslant 3$ where $f(u)$ is superlinear and nonnegative. The solution blows up on a surface $t = {\phi _\varepsilon }(x)$. Denote by $t = \phi (x)$ the blow-up surface corresponding to $v'' = f(v)$. It is proved that $|{\phi _\varepsilon }(x) - \phi (x)| \leqslant C{\varepsilon ^2}$, $|\nabla ({\phi _\varepsilon }(x) - \phi (x))| \leqslant C{\varepsilon ^2}$ in a neighborhood of any point ${x_0}$ where $\phi ({x_0}) < \infty$.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 308 (1988), 349-367
- MSC: Primary 35L70; Secondary 35B40
- DOI: https://doi.org/10.1090/S0002-9947-1988-0946448-7
- MathSciNet review: 946448