Uniform estimates for solutions of nonlinear focusing damped wave equations

2024/03/11 by Thomas Perrin, Perrin, Thomas
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2403.06541

openalex publication_date 2024/03/11 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28

Abstract

For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result applies in particular to the case of a cubic equation on a bounded domain of dimension 3.

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• Profiles of bounded radial solutions of the focusing, energy-critical wave equation
• Long time dynamics for damped Klein-Gordon equations
• Scattering for radial, bounded solutions of focusing supercritical wave equations
• Asymptotics of solutions with a compactness property for the nonlinear damped Klein-Gordon equation