Theory of damped wave models with integrable and decaying in time speed of propagation-Reference-Cited by-同舟云学术

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

Published:2016-06 Issue:02 Volume:13 Page:417-439
ISSN:0219-8916
Container-title:Journal of Hyperbolic Differential Equations
language:en
Short-container-title:J. Hyper. Differential Equations

Author:

Ebert Marcelo Rempel¹,Reissig Michael²

Affiliation:

1. Departamento de Computação e Matemática, Universidade de São Paulo (USP), FFCLRP, Av. dos Bandeirantes, 3900, Ribeirão Preto, São Paulo, 14040-901, Brazil

2. Faculty of Mathematics and Informatics, Institute of Applied Analysis, Technical University Bergakademie Freiberg, Prüferstr.9, Freiberg, 09596 Germany

Abstract

We study the Cauchy problem for damped wave equations with a time-dependent propagation speed and dissipation. The model of interest is [Formula: see text] We assume [Formula: see text]. Then we propose a classification of dissipation terms in non-effective 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219891616500132

Reference12 articles.

1. The Interplay Between Time-dependent Speed of Propagation and Dissipation in Wave Models

2. Energy estimates at infinity for hyperbolic equations with oscillating coefficients

3. A class of dissipative wave equations with time-dependent speed and damping

4. On the energy estimates of the wave equation with time dependent propagation speed asymptotically monotone functions

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