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The blow-up surface for nonlinear wave equations with small spatial velocity
1988
Transactions of the American Mathematical Society
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Consider the Cauchy problem for utt -e2Au = f(u) in space dimension < 3 where f{u) is superlinear and nonnegative. The solution blows up on a surface t = 4>e(x). Denote by t = d>(x) the blow-up surface corresponding to v" = /(«). It is proved that \e(x)-£(x) -tp(x))\ < Ce2 in a neighborhood of any point zrj where (p(xo) < oo.
doi:10.1090/s0002-9947-1988-0946448-7
fatcat:o52ri4xfz5drbpzmj5yo5ktcpi