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<p>This paper focuses on establishing the existence of a weak solution for a class of nonlinear double-phase parabolic equations with logarithmic convection terms, subject to certain conditions on the data. The proof relies on Young measure theory and Galerkin’s approximation method in Musielak–Orlicz Sobolev spaces with variable exponents. The methodology presented here can be naturally extended to a broader class of unbalanced double-phase problems that include logarithmic perturbations and gradient dependence on the right-hand side.</p>

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On a class of nonlinear parabolic problems with logarithmic double-phase operators and convection terms

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Hasna Moujani,
  • Ali El Mfadel,
  • Abderrazak Kassidi,
  • M’hamed Elomari

摘要

This paper focuses on establishing the existence of a weak solution for a class of nonlinear double-phase parabolic equations with logarithmic convection terms, subject to certain conditions on the data. The proof relies on Young measure theory and Galerkin’s approximation method in Musielak–Orlicz Sobolev spaces with variable exponents. The methodology presented here can be naturally extended to a broader class of unbalanced double-phase problems that include logarithmic perturbations and gradient dependence on the right-hand side.