Mathematics of nonlinear acoustics

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.