| Full text | |
| Author(s): |
Ebert, Marcelo Rempel
;
Reissig, Michael
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Hyperbolic Differential Equations; v. 13, n. 2, p. 417-439, JUN 2016. |
| Web of Science Citations: | 6 |
| Abstract | |
We study the Cauchy problem for damped wave equations with a timedependent propagation speed and dissipation. The model of interest is u(tt) - a(t)(2) Delta u + b(t)u(t) = 0, u(0, x) = u(0)(x), u(t)(0, x) = u(1)(x). We assume a is an element of L-1(R+). Then we propose a classification of dissipation terms in noneffective and effective. In each case we derive estimates for kinetic and elastic type energies by developing a suitable WKB analysis. Moreover, we show optimality of results by the aid of scale-invariant models. Finally, we explain by an example that in some estimates a loss of regularity appears. (AU) | |
| FAPESP's process: | 13/20297-8 - Decay estimates for hyperbolic partial differential equations in the L^p-L^q framework |
| Grantee: | Marcelo Rempel Ebert |
| Support type: | Scholarships abroad - Research |