Inhomogeneous Parabolic Neumann Problems

2011/08/31 by Nittka, Robin · 2 citations
#35B65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35K20 #Secondary: 35B15

paper · doi:10.48550/arxiv.1108.6227

Abstract

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.

Cited by

• On the global existence and uniform-in-time bounds for three-component reaction-diffusion systems with mass control and polynomial growth
• Diffusion over ramified domains: solvability and fine regularity

Related

• Quasilinear elliptic and parabolic Robin problems on Lipschitz domains
• Weak solutions to the parabolic p-Laplace equation in a moving domain under a Neumann type boundary condition
• Novel exact solutions for PDEs with mixed boundary conditions
• Perturbation theory for the parabolic Regularity and Neumann problem
• On Neumann problems for elliptic and parabolic equations on bounded manifolds