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

Petronela Radu

Applicationes Mathematicae (2008)

  • Volume: 35, Issue: 3, page 355-378
  • ISSN: 1233-7234

Abstract

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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 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.

How to cite

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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 35.3 (2008): 355-378. <http://eudml.org/doc/280043>.

@article{PetronelaRadu2008,
abstract = {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.},
author = {Petronela Radu},
journal = {Applicationes Mathematicae},
keywords = {wave equation; local existence; finite speed of propagation; nonlinear damping; interior source},
language = {eng},
number = {3},
pages = {355-378},
title = {Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms},
url = {http://eudml.org/doc/280043},
volume = {35},
year = {2008},
}

TY - JOUR
AU - Petronela Radu
TI - Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms
JO - Applicationes Mathematicae
PY - 2008
VL - 35
IS - 3
SP - 355
EP - 378
AB - 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.
LA - eng
KW - wave equation; local existence; finite speed of propagation; nonlinear damping; interior source
UR - http://eudml.org/doc/280043
ER -

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