Delayed singularity formation for solutions of nonlinear partial differential equations in higher dimensions.

@article{John1976DelayedSF,
  title={Delayed singularity formation for solutions of nonlinear partial differential equations in higher dimensions.},
  author={F M John},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1976},
  volume={73 2},
  pages={281-2}
}
  • F M John
  • Published 1976 in
    Proceedings of the National Academy of Sciences…
Strict solutions u of genuinely nonlinear homogeneous hyperbolic equations in two independent variables with initial data f(x) of compact support become singular after a time interval of order parallelf parallel(-1). In higher dimensions solutions initially of compact support are likely to have life expectancies of orders parallelf parallel(-2+epsilon) at least. This is proved for the special case of solutions u(x(1),..., x(n), t) of a second order equation u(tt) = Sigma(i,j)a(ij)u(xixj), where… CONTINUE READING