The Existence of Entropy Solutions for a Class of Parabolic Equations

Zengfei Chen and Bingliang Shen ()
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Zengfei Chen: Zhejiang College, Shanghai University of Finance & Economics, Jinhua 321013, China
Bingliang Shen: Zhejiang College, Shanghai University of Finance & Economics, Jinhua 321013, China

Mathematics, 2023, vol. 11, issue 17, 1-24

Abstract: The existence and uniqueness of entropy solutions for a class of parabolic equations involving a p ( x ) -Laplace operator are investigated. We first prove existence of the global weak solution for the p ( x ) -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 p ( x ) -Laplacian equations with irregular initial data in whole space is also obtained.

Keywords: variable exponent; entropy solution; truncation function; variational methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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