Generic regularity of conservative solutions to a nonlinear wave equation

By Alberto Bressan, Geng Chen. 2015

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Abstract The paper is concerned with conservative solutions to the nonlinear wave equation u t t − c ( u ) ( c ( u ) u x ) x = 0 . For an open dense set of C 3 initial data, we prove that the solution is piecewise smooth in the t–x plane, while the gradient u x 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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5dfe2315d6ee90c25d0f77db010ec73f6c6b793c