Year: 2026
Type: preprint
Abstract: We consider the Cauchy problem for semilinear classical damped wave equations with general nonnegative nondecreasing nonlinearities, without imposing a modulus-of-continuity structure or convexity. A Dini-type integral condition expressed directly in terms of the nonlinearity gives small data global in-time existence and extends the nonlinear framework of Ebert--Girardi--Reissig [Math. Ann. 378 (2020), 1311--1326]. When this Dini-type integral diverges and the effective total mass of the initial data is positive, convergence of the Keller--Osserman tail integral is necessary and sufficient for finite-time blow-up of the maximal mild Sobolev solution, particularly, divergence of the tail integral gives global grow-up. The resulting integral criteria distinguish the contributions of the nonlinearity near zero and at infinity in governing small data global in-time existence with diffusion decay, global grow-up, and finite-time blow-up.
Source: arXiv (Cornell University)
Author: Chen, Wenhui
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2469264322, G7952596114
OpenAlex ID: W7214225391