Hyung Ju Hwang, Juhi Jang, Juan J. L. Velazquez
Published 2013-11-19Version 1
We study the initial-boundary value problem for the Fokker-Planck equation in an interval with absorbing boundary conditions. We develop a theory of well-posedness of classical solutions for the problem. We also prove that the resulting solutions decay exponentially for long times. To prove these results we obtain several crucial estimates, which include hypoellipticity away from the singular set for the Fokker-Planck equation with absorbing boundary conditions, as well as the Holder continuity of the solutions up to the singular set.
Local existence results for the Westervelt equation with nonlinear damping and Neumann as well as absorbing boundary conditions
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