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Wellposedness and long time behavior for a general class of Moore-Gibson-Thompson equations

Nicaise Serge, Bounadja Hizia

Control and Cybernetics

2020

Vol. 49, No. 3

245--276

We consider the well-posedness and the long time behavior of third order in time linear evolution equations, general and abstract version of the Moore-Gibson-Thompson system. We find sufficient but strong conditions that guarantee the exponential decay of the system and present some illustrative examples. 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 weaker conditions that guarantee exponential, polynomial or even logarithmic decay of the solution of the Moore-Gibson-Thompson system in a bounded domain of Rn, n ≥ 1.