Stability of anisotropic parabolic equations without boundary conditions
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In this article, we consider the equation
ut = N∑i=1 (αi(x)|uxi |pi(x)-2 uxi)xi,
with αi(x), pi(x) ∈ C1 (Ω̅) and pi(x) > 1. Where αi(x) = 0 if x ∈ ∂Ω, and αi(x) > 0 if x ∈ Ω, without any boundary conditions. We propose an analytical method for studying the stability of weak solutions. We also study the uniqueness of a weak solution, and establish its stability under certain conditions.
CitationZhan, H., & Feng, Z. (2020). Stability of anisotropic parabolic equations without boundary conditions. Electronic Journal of Differential Equations, 2020(74), pp. 1-14.
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