TY - JOUR
T1 - Qualitative properties of solutions to structurally damped σevolution models with time increasing coefficient in the dissipation
AU - Mezadek, Mohamed Kainane
AU - Reissig, Michael
AU - Ozawa, Tohru
PY - 2015/5/1
Y1 - 2015/5/1
N2 - 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.
AB - 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.
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M3 - Article
AN - SCOPUS:84964915733
VL - 20
SP - 433
EP - 462
JO - Advances in Differential Equations
JF - Advances in Differential Equations
SN - 1079-9389
IS - 5-6
ER -