Well-posedness and longtime behavior for the Westervelt equation with absorbing boundary conditions of order zero

  title={Well-posedness and longtime behavior for the Westervelt equation with absorbing boundary conditions of order zero},
  author={Gieri Simonett and Mathias Wilke},
  journal={Journal of Evolution Equations},
We investigate the Westervelt equation from nonlinear acoustics, subject to nonlinear absorbing boundary conditions of order zero, which were recently proposed in Kaltenbacher and Shevchenko (Discrete Contin Dyn Syst 1000–1008, 2015), Shevchenko and Kaltenbacher (J Comput Phys 302:200–221, 2015). We apply the concept of maximal regularity of type Lp to prove global well-posedness for small initial data. Moreover, we show that the solutions regularize instantaneously, which means that they are C… 

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Boundary Observability and Stabilization for Westervelt Type Wave Equations without Interior Damping

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Nonlinear analytic semiflows

  • S. Angenent
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 1990
Synopsis In this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems (x′(t) = f(x(t))), and quasilinear initial value problems (x′(t)=A(x(t))x(t) +