Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms

• Autorzy: Petronela Radu
• Języki publikacji: EN

Abstrakty

EN

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 H¹(Ω) into L²(Ω) 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.

Kategorie tematyczne

• 35L05: Wave equation
• 35L20: Initial-boundary value problems for second-order hyperbolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2008
• Tom: 35
• Numer: 3
• Strony: 355-378

Daty

wydano

2008

Twórcy

autor

Petronela Radu

• Department of Mathematics, University of Nebraska-Lincoln, 203 Avery Hall, Lincoln, NE 68588-0130, U.S.A.

Identyfikatory

DOI

10.4064/am35-3-7