Zhan, HuashuiFeng, Zhaosheng2021-10-012021-10-012020-07-15Zhan, H., & Feng, Z. (2020). Stability of anisotropic parabolic equations without boundary conditions. <i>Electronic Journal of Differential Equations, 2020</i>(74), pp. 1-14.1072-6691https://hdl.handle.net/10877/14581In 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.Text14 pages1 file (.pdf)enAttribution 4.0 InternationalParabolic equationBoundary conditionStabilityHolder inequalityArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.