Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and damping

2008/11/13 by Lorena Bociu, Bociu, Lorena, Petronela Radu +1
Engineering · Mathematics · #35L05 #35L15 #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0811.2151

openalex publication_date 2008/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show existence of finite energy solutions for the Cauchy problem associated with a semilinear wave equation with interior damping and supercritical source terms. The main contribution consists in dealing with super-supercritical source terms (terms of the order of |u|^p with p≥ 5 in n=3 dimensions), an open and highly recognized problem in the literature on nonlinear wave equations.

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