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arXiv · 2608.04671

Global existence of solutions for nonlinear damped wave equations in an exterior domain with nonlinearities of derivative type

Tuan Anh Dao·Dinh Van Duong·Masahiro Ikeda
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Abstract

In this paper, we are interested in considering the semi-linear damped wave equation with the power nonlinearity of derivative type in $2$D exterior domains to indicate the global (in time) existence of small data solutions, which has never appeared in previous studies. Our proof is based on constructing a judicious time-weighted function space and demonstrating nonlinear estimates compatible with fractional powers of the Dirichlet Laplacian linked to the semigroup decay structure. Moreover, the large time behavior of the time derivative of the obtained global solutions and its sharp estimate are also discussed in this paper.

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Tuan Anh Dao, Dinh Van Duong, Masahiro Ikeda. 2026-08-05. Global existence of solutions for nonlinear damped wave equations in an exterior domain with nonlinearities of derivative type. https://arxiv.org/abs/2608.04671

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