Some remarks on the asymptotic profile of solutions to structurally damped σ-evolution equations

2019/08/22 by Dao, Tuan Anh
#35L30 #35M11 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35B40 #Secondary: 35G10

paper · doi:10.48550/arxiv.1908.08492

Abstract

In this paper, we are interested in analyzing the asymptotic profiles of solutions to the Cauchy problem for linear structurally damped σ-evolution equations in L²-sense. Depending on the parameters σ and δ we would like to not only indicate approximation formula of solutions but also recognize the optimality of their decay rates as well in the distinct cases of parabolic like damping and σ-evolution like damping. Moreover, such results are also discussed when we mix these two kinds of damping terms in a σ-evolution equation to investigate how each of them affects the asymptotic profile of solutions.

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