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}
}
• Published 7 September 2012
• Mathematics
• arXiv: Analysis of PDEs
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…
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