Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation
Analysis of PDEs
2011-05-17 v1
Abstract
We study the nonlinear inhomogeneous wave equation in one space dimension: . 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.
Cite
@article{arxiv.1105.3174,
title = {Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation},
author = {Geng Chen and Robin Young},
journal= {arXiv preprint arXiv:1105.3174},
year = {2011}
}