Global existence of small data solutions for wave models with super-exponential propagation speed

Bui, Tang Bao Ngoc; Reissig, Michael

doi:10.1016/j.na.2014.10.035

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Remark 11. The recent papers [3] and [4] are devoted to studying the following Cauchy problem for semi-linear wave models with effective dissipation: u tt − a 2 (t)∆u + b(t)u t = |u| p , (t, x) ∈ [0, ∞) × R n , u(0, x) = u 0 (x), u t (0, x) = u 1 (x), x ∈ R n .…”

Section: Concluding Remarks and Open Problemsmentioning

confidence: 99%

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The Influence of Oscillations on Energy Estimates for Damped Wave Models with Time-dependent Propagation Speed and Dissipation

Aslan

Reissig

2019

Springer Proceedings in Mathematics &Amp; Statistics

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The aim of this paper is to derive higher order energy estimates for solutions to the Cauchy problem for damped wave models with time-dependent propagation speed and dissipation. The model of interest isThe coefficients λ = λ(t) and ρ = ρ(t) are shape functions and ω = ω(t) is a bounded oscillating function. If ω(t) ≡ 1 and ρ(t)ut is an effective dissipation term, then L 2 − L 2 energy estimates are proved in [2]. In contrast, the main goal of the present paper is to generalize the previous results to coefficients including an oscillating function in the time-dependent coefficients. We will explain how the interplay between the shape functions and oscillating behavior of the coefficient ω = ω(t) will influence energy estimates.

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Section: Concluding Remarks and Open Problemsmentioning

confidence: 99%

“…Remark 11. The recent papers [3] and [4] are devoted to studying the following Cauchy problem for semi-linear wave models with effective dissipation:…”

Section: ⊓ ⊔mentioning

confidence: 99%