Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation

Details Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation

2011-05-16

arxiv.org/abs/1105.3174v1

Mathematics

Analysis of PDEs

Scientific paper

We study the nonlinear inhomogeneous wave equation in one space dimension: $v_{tt} - T(v,x)_{xx} = 0$. By constructing some "decoupled" Riccati type equations for smooth solutions, we provide a singularity formation result without restrictions on the total variation of unknown, which generalize earlier singularity results of Lax and the first author. These results are applied to several one-dimensional hyperbolic models, such as compressible Euler flows with a general pressure law, elasticity in an inhomogeneous medium, transverse MHD flow, and compressible flow in a variable area duct.

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