# Global well-posedness and exponential stability for Kuznetsov's equation in L_p-spaces

@article{Meyer2012GlobalWA, title={Global well-posedness and exponential stability for Kuznetsov's equation in L\_p-spaces}, author={Stefan Meyer and Mathias Wilke}, journal={arXiv: Analysis of PDEs}, year={2012} }

We investigate a quasilinear initial-boundary value problem for Kuznetsov's equation with non-homogeneous Dirichlet boundary conditions. This is a model in nonlinear acoustics which describes the propagation of sound in fluidic media with applications in medical ultrasound. We prove that there exists a unique global solution which depends continuously on the sufficiently small data and that the solution and its temporal derivatives converge at an exponential rate as time tends to infinity…

## 13 Citations

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### A P ] 8 O ct 2 01 8 Cauchy Problem for the Kuznetsov Equation

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We prove global solvability of the third-order in time Jordan–More–Gibson–Thompson acoustic wave equation with memory in $${\mathbb {R}}^n$$
R
n
, where $$n \ge 3$$
n
≥
3
. This…

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