Thresholds for low regularity solutions to wave equations with structural damping

2019/07/22 by Tomonori Fukushima, Fukushima, Tomonori, Ryo Ikehata +3
Mathematics · Engineering · Computer Science · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1907.09299

Abstract

We study the asymptotic behavior of solutions to wave equations with a structural damping term u_tt-Δu+Δ² u_t=0, u(0,x)=u₀(x), u_t(0,x)=u₁(x), in the whole space. New thresholds are reported in this paper that indicate which of the diffusion wave property and the non-diffusive structure dominates in low regularity cases. We develop to that end the previous author's research in 2019 where they have proposed a threshold that expresses whether the parabolic-like property or the wave-like property strongly appears in the solution to some regularity-loss type dissipative wave equation.

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