Existence and regularity of global attractors for a Kirchhoff wave equation with strong damping and memory

2023/03/25 by Yang, Bin, Qin, Yuming, Miranville, Alain +1
#35B40 #35B41 #35B65 #35L05 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.14387

Abstract

This paper is concerned with the existence and regularity of global attractor \mathcal A for a Kirchhoff wave equation with strong damping and memory in the weighted time-dependent spaces \mathcal H and \mathcal H¹, respectively. In order to obtain the existence of \mathcal A, we mainly use the energy method in the priori estimations, and then verify the asymptotic compactness of the semigroup by the method of contraction function. Finally, by decomposing the weak solutions into two parts and some elaborate calculations, we prove the regularity of \mathcal A.

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