WIAS Preprint No. 2094, (2015)

On the strongly damped wave equation with constraint



Authors

  • Bonetti, Elena
  • Rocca, Elisabetta
  • Schimperna, Giulio
  • Scala, Riccardo

2010 Mathematics Subject Classification

  • 35L05 74D10 47H05 46A20

Keywords

  • wave equation, strong damping, weak solution, maximal monotone operator, duality.

DOI

10.20347/WIAS.PREPRINT.2094

Abstract

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.

Appeared in

  • Comm. Partial Differential Equations, 42 (2017), pp. 1042-1064.

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