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Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters
- Source :
- JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
- Publication Year :
- 2017
-
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.<br />23 pages
- Subjects :
- Acoustic equation
General Mathematics
math-ph
Mathematics, Applied
FOS: Physical sciences
42A85, 44A35
0101 Pure Mathematics
math.MP
Mathematics - Analysis of PDEs
SYSTEMS
0102 Applied Mathematics
EQUATION
FOS: Mathematics
math.AP
Mathematical Physics
Cauchy problem
Science & Technology
TIME-DEPENDENT DISSIPATION
Shallow water
Mathematical Physics (math-ph)
Mathematics and Statistics
Dissipative wave equation
Physical Sciences
Mathematics
Analysis of PDEs (math.AP)
Subjects
Details
- Language :
- English
- ISSN :
- 00217824
- Database :
- OpenAIRE
- Journal :
- JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
- Accession number :
- edsair.doi.dedup.....d20bb196ec212481f889519d75f0f7ca