The Existence of Entropy Solutions for a Class of Parabolic Equations - Zengfei Chen; Bingliang Shen (Mathematics, 2023)
The existence and uniqueness of entropy solutions for a class of parabolic equations involving a <semantics>p(x)</semantics>-Laplace operator are investigated. We first prove existence of the global weak solution for the <semantics>p(x)</semantics>-Laplacian equations with regular initial data via the difference and variation methods as well as the standard domain expansion technique. Then, by constructing and solving a related approximation problem, the entropy solution for the <semantics>p(x)</semantics>-Laplacian equations with irregular initial data in whole space is also obtained.