Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation

Abstract

The paper is concerned with conservative solutions to the nonlinear wave equation utt−c(u) ( c(u)ux ) x = 0. For an open dense set of C initial data, we prove that the solution is piecewise smooth in the t-x plane, while the gradient ux can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom’s transversality theorem.

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Cite this paper

@inproceedings{Bressan2015GenericRO, title={Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation}, author={Alberto Bressan and Geng - Fung Chen}, year={2015} }