Geodesic
Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms
Petronela Radu1
1 Department of Mathematics University of Nebraska-Lincoln 203 Avery Hall Lincoln, NE 68588-0130, U.S.A.
Applicationes Mathematicae, Tome 35 (2008) no. 3, pp. 355-378 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am35-3-7
Keywords: local existence solutions initial boundary value problem corresponding semilinear wave equation interior damping source terms difficulty dealing these competitive forces comes the source term locally lipschitz function omega omega typically assumed literature strategy behind proof based physics problem does damping present equation arguments natural adaptable other settings other pdes

Petronela Radu 1

1 Department of Mathematics University of Nebraska-Lincoln 203 Avery Hall Lincoln, NE 68588-0130, U.S.A. 
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 problem for a semilinear wave equation with
 damping and source terms
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Petronela Radu. Weak solutions to the initial boundary value
 problem for a semilinear wave equation with
 damping and source terms. Applicationes Mathematicae, Tome 35 (2008) no. 3, pp. 355-378. doi: 10.4064/am35-3-7

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