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 our 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.
On the strongly damped wave equation with constraint / E. Bonetti, E. Rocca, R. Scala, G. Schimperna. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 42:7(2017), pp. 1042-1064. [10.1080/03605302.2017.1345937]
On the strongly damped wave equation with constraint
E. BonettiPrimo
;
2017
Abstract
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 our 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.
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