Mathematics of nonlinear acoustics

Barbara  Kaltenbacher

doi:10.3934/eect.2015.4.447

Article Contents

2015, Volume 4, Issue 4: 447-491. Doi: 10.3934/eect.2015.4.447 open access

This issue Previous Article On the Cauchy problem for the Schrödinger-Hartree equation Next Article Stability of nonlinear differential systems with delay

Mathematics of nonlinear acoustics

Barbara Kaltenbacher^1,

1.
Alpen-Adria-Universität Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt

Received: April 30, 2015

Revised: September 30, 2015

Published: November 2015

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Abstract

The aim of this paper is to highlight some recent developments and outcomes in the mathematical analysis of partial differential equations describing nonlinear sound propagation. Here the emphasis lies on well-posedness and decay results, first of all for the classical models of nonlinear acoustics, later on also for some higher order models. Besides quoting results, we also try to give an idea on their derivation by showning some of the crucial energy estimates. A section is devoted to optimization problems arising in the practical use of high intensity ultrasound.
While this review puts a certain focus on results obtained in the context of the mentioned FWF project, we also provide some important additional references (although certainly not all of them) for interesting further reading.

Keywords:

Mathematics Subject Classification: Primary: 35L72, 35L77; Secondary: 35L80, 35B40, 49K20, 49Q10.

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