Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation

2011/05/16 by Geng Chen, Chen, Geng, Robin Young +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1105.3174

openalex publication_date 2011/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Formation of singularities in one‐dimensional nonlinear wave propagation

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