Highly Influenced

@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} }

- 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

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