On the strongly damped wave equation with constraint

A weak formulation for the so-called semilinear strongly damped wave equation with constraint is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in Sobolev-Bochner spaces, aimed at providing a suitable "relaxation" of the constraint term. A global in time existence result is proved under the natural condition that the initial data have finite "physical" energy.

Keywords

Wave equation, strong damping, weak solution, maximal monotone operator, duality.

URI

https://doi.org/10.34657/2916
https://oa.tib.eu/renate/handle/123456789/2786

Citation

Bonetti, E., Rocca, E., Schimperna, G., & Scala, R. (2015). On the strongly damped wave equation with constraint (Vol. 2094). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.

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Mathematik

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