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The Existence of Entropy Solutions for a Class of Parabolic Equations

Author

Listed:
  • Zengfei Chen

    (Zhejiang College, Shanghai University of Finance & Economics, Jinhua 321013, China)

  • Bingliang Shen

    (Zhejiang College, Shanghai University of Finance & Economics, Jinhua 321013, China)

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.

Suggested Citation

  • Zengfei Chen & Bingliang Shen, 2023. "The Existence of Entropy Solutions for a Class of Parabolic Equations," Mathematics, MDPI, vol. 11(17), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3753-:d:1230302
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    References listed on IDEAS

    as
    1. Azroul, E. & Benboubker, M.B. & Rhoudaf, M., 2014. "On some p(x)-quasilinear problem with right-hand side measure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 117-130.
    2. Weihong Xie & Haibo Chen, 2018. "Existence and multiplicity of solutions for p(x)‐Laplacian equations in RN," Mathematische Nachrichten, Wiley Blackwell, vol. 291(16), pages 2476-2488, November.
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