Global Well Posedness for Damped Wave Models with Damping in the Memory (European Journal of Pure and Applied Mathematics, 2025)
This paper aims to study the Cauchy problem for damped wave models with a dissipative memory term. The main objective is to establish global (in time) well-posedness results for both energy solutions and higher-regularity solutions, determine the critical exponent in the Fujita sense, and investigate the influence of nonlinear memory on the Fujita exponent. Using modern tools from harmonic analysis and the Banach fixed point method, we show several results by taking into consideration different regularity properties of the initial data.
Keywords: damped wave equation; nonlinear memory; Cauchy problem; energy solutions; Matsumura type estimates; fixed point theorem