Qualitative properties of solutions to structurally damped σevolution models with time increasing coefficient in the dissipation

Mohamed Kainane Mezadek, Michael Reissig, Tohru Ozawa

研究成果: Article

3 引用 (Scopus)

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The goal of this paper is to study qualitative properties of solutions to the Cauchy problem for structurally damped σevolution models utt + (-δ)σu + b(t)(-δ)δut = 0; u(0; x) = u0(x); ut(0; x) = u1(x); where σ > 1, δ (0, σ), and the dissipation coecient b = b(t) is a timedependent and strictly increasing positive function. On the one hand, we are interested in Lp - Lq estimates for the energies of higher order. On the other hand, we are interested in Gevrey smoothing properties of solutions. Finally, we prove the optimality of decay by using scaleinvariant models. The main tool of our considerations is a related WKB-analysis.

元の言語English
ページ(範囲)433-462
ページ数30
ジャーナルAdvances in Differential Equations
20
発行部数5-6
出版物ステータスPublished - 2015 5 1
外部発表Yes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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