Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters

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Title: Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters
Authors: Munoz, JC
Ruzhansky, M
Tokmagambetov, N
Item Type: Journal Article
Abstract: In this paper we consider an acoustic problem of wave propagation through a discontinuous medium. The problem is reduced to the dissipative wave equation with distributional dissipation. We show that this problem has a so-called very weak solution, we analyse its properties and illustrate the theoretical results through some numerical simulations by approximating the solutions to the full dissipative model for a particular synthetic piecewise continuous medium. In particular, we discover numerically a very interesting phenomenon of the appearance of a new wave at the singular point. For the acoustic problem this can be interpreted as an echo effect at the discontinuity interface of the medium.
Issue Date: 1-Mar-2019
Date of Acceptance: 16-Aug-2018
URI: http://hdl.handle.net/10044/1/63541
DOI: https://dx.doi.org/10.1016/j.matpur.2019.01.012
ISSN: 0021-7824
Publisher: Elsevier
Start Page: 127
End Page: 147
Journal / Book Title: Journal de Mathématiques Pures et Appliquées
Volume: 123
Copyright Statement: ©2019 The Authors. Published by Elsevier Masson SAS. This is an open access article under the CC-BY license (http://creativecommons.org/licenses/by/4.0/)
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/K039407/1
RPG-2014-002
EP/R003025/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Acoustic equation
Shallow water
Cauchy problem
Dissipative wave equation
TIME-DEPENDENT DISSIPATION
EQUATION
SYSTEMS
math.AP
math.AP
math-ph
math.MP
42A85, 44A35
math.AP
math.AP
math-ph
math.MP
42A85, 44A35
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Notes: 23 pages
Publication Status: Published
Online Publication Date: 2019-01-24
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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