Entropy solutions of exterior problems for nonlinear degenerate parabolic equations with nonhomogeneous boundary condition
Date
2016-03-18
Authors
Zhang, Li
Su, Ning
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we consider the exterior problem for the nonlinear degenerate parabolic equation
ut - ∆b(u) + ∇ ⋅ ɸ(u) = F(u), (t, x) ∈ (0, T) x Ω,
Ω is the exterior domain of Ω0 (a closed bounded domain in ℝN with its boundary Γ ∈ C1,1), b is non-decreasing and Lipschitz continuous, ɸ = (φ1,…,φN) is vectorial continuous, and F is Lipschitz continuous. In the nonhomogeneous boundary condition where b(u) = b(ɑ) on (0, T) x Γ, we establish the comparison and uniqueness, the existence using penalized method.
Description
Keywords
Degenerate parabolic equation, Exterior problem, Nonlinear, Entropy solution
Citation
Zhang, L., & Su, N. (2016). Entropy solutions of exterior problems for nonlinear degenerate parabolic equations with nonhomogeneous boundary condition. <i>Electronic Journal of Differential Equations, 2016</i>(77), pp. 1-11.
Rights
Attribution 4.0 International