Inhomogeneous Parabolic Neumann Problems

Details Inhomogeneous Parabolic Neumann Problems Inhomogeneous Parabolic Neumann Problems

2011-08-31

arxiv.org/abs/1108.6227v1

Mathematics

Analysis of PDEs

29 pages

Scientific paper

We study second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of the parabolic cylinder. Under natural assumptions on the coefficients and the inhomogeneity we can also prove convergence to an equilibrium or asymptotic almost periodicity.

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