| Contents |
| The goal of the lecture is an analysis of qualitative properties of solutions to the Cauchy problem for structurally damped evolution models
u_{tt} + (-\Delta)^\sigma u + b(t)(-\Delta}^\delta u_t=0,\,\,u(0,x)=u_0(x),\,\,u_t(0,x)=u_1(x).
The main concern are estimates of energies of higher order not necessarily on the conjugate line.
Here $L^1-L^1$ estimates are of special interest. Moreover, we present Gevrey smoothing.
By studying scale-invariant models we prove optimality of our results. The main tools are a refined WKB-analysis of hyperbolic-elliptic coupled type, theory of Fourier multipliers and modified Bessel functions. Finally, parameter dependent Cauchy problems are discussed. |
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