JournalspmVol. 78, No. 3/4pp. 391–422

Well-posedness and long time behavior for a general class of Moore–Gibson–Thompson equations with a memory

  • Serge Nicaise

    Université Polytechnique Hauts-de-France, Valenciennes, France
  • Hizia Bounadja

    Ferhat Abbas University, Sétif, Algeria
Well-posedness and long time behavior for a general class of Moore–Gibson–Thompson equations with a memory cover
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Abstract

We consider the well-posedness and the long time behavior of the Moore– Gibson–Thompson equation with memory in the critical case. We first find general sufficient conditions that guarantee a (optimal) polynomial decay of the system. Then by comparing the behavior of the resolvent of the Moore–Gibson–Thompson system with the one of the resolvent of the wave equation with a frictional interior damping, we furnish a stronger polynomial decay of the solution.

Cite this article

Serge Nicaise, Hizia Bounadja, Well-posedness and long time behavior for a general class of Moore–Gibson–Thompson equations with a memory. Port. Math. 78 (2021), no. 3/4, pp. 391–422

DOI 10.4171/PM/2074