2014/07/04 by Alberto Bressan, Tao Huang, Bressan, Alberto +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.AP
paper · pdf · doi:10.48550/arxiv.1407.1220
arxiv created 2014/07/04 · openalex publication_date 2014/07/04 · arxiv updated 2014/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with the conservative case, here the source terms are discontinuous and the discontinuities are not always crossed transversally. Solutions to the semilinear system are obtained by an approximation argument, relying on Kolmogorov's compactness theorem. Reverting to the original variables, one recovers a solution to the nonlinear wave equation where the total energy is a monotone decreasing function of time.