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

Mohamed Kainane Mezadek, Michael Reissig, Tohru Ozawa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)433-462
Number of pages30
JournalAdvances in Differential Equations
Volume20
Issue number5-6
Publication statusPublished - 2015 May 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Qualitative properties of solutions to structurally damped σevolution models with time increasing coefficient in the dissipation'. Together they form a unique fingerprint.

  • Cite this