Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms
Tom 35 / 2008
Applicationes Mathematicae 35 (2008), 355-378
MSC: Primary 35L05; Secondary 35L20.
DOI: 10.4064/am35-3-7
Streszczenie
We show local existence of solutions to the initial boundary value problem corresponding to a semilinear wave equation with interior damping and source terms. The difficulty in dealing with these two competitive forces comes from the fact that the source term is not a locally Lipschitz function from $H^{1}({ \Omega })$ into $L^2({\Omega })$ as typically assumed in the literature. The strategy behind the proof is based on the physics of the problem, so it does not use the damping present in the equation. The arguments are natural and adaptable to other settings/other PDEs.
