On the strongly damped wave equation with constraint
- Bonetti, Elena
- Rocca, Elisabetta
- Schimperna, Giulio
- Scala, Riccardo
2010 Mathematics Subject Classification
- 35L05 74D10 47H05 46A20
- wave equation, strong damping, weak solution, maximal monotone operator, duality.
A weak formulation for the so-called semilinear strongly damped wave equation with constraint is introduced and a corresponding notion of solution is de?ned. 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.
- Comm. Partial Differential Equations, 42 (2017), pp. 1042-1064.