Uniform estimates for solutions of nonlinear focusing damped wave equations

Published 11 Mar 2024 in math.AP | (2403.06541v1)

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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Thomas Perrin

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