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 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.
Bonetti, E., Rocca, E., Scala, R., Schimperna, G. (2017). On the strongly damped wave equation with constraint. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 42(7), 1042-1064 [10.1080/03605302.2017.1345937].
On the strongly damped wave equation with constraint
Scala R;
2017-01-01
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 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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https://hdl.handle.net/11365/1087430