On the solutions for nonlinear wave equations with localized dissipations in exterior domains. (English) Zbl 1342.35165

Ei, Shin-Ichiro (ed.) et al., Nonlinear dynamics in partial differential equations. Proceedings of the 4th MSJ-SI international conference, Kyushu, Japan, September 12–21, 2011. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-022-8/hbk). Advanced Studies in Pure Mathematics 64, 289-294 (2015).
Summary: The Cauchy problem for nonlinear wave equations with localized dissipation is considered in exterior domains outside of compact obstacles in three spatial dimensions. Under the null conditions for the quadratic nonlinear terms, the global solutions are shown for sufficiently small data. The solutions which have different propagation speeds are considered.
For the entire collection see [Zbl 1321.35002].


35L20 Initial-boundary value problems for second-order hyperbolic equations
35L71 Second-order semilinear hyperbolic equations