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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Theory of damped wave models with integrable and decaying in time speed of propagation

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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