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<p>We investigate a class of nonlinear parabolic problems with nonlinear boundary conditions governed by a logarithmic double-phase operator in the framework of Musielak–Orlicz Sobolev spaces with variable exponents. Using the Galerkin approximation method and Young measure theory, we establish the existence of weak solutions under general and natural growth conditions on the nonlinear terms. Our approach extends the existing theory for variable exponent problems and provides a robust framework for studying nonhomogeneous and highly irregular diffusion phenomena in nonlinear analysis.</p>

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Nonlinear parabolic problems with logarithmic double-phase operators in variable exponent Musielak–Orlicz spaces

  • 期刊论文

  • 发表日期：

    2026年1月16日

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

摘要

We investigate a class of nonlinear parabolic problems with nonlinear boundary conditions governed by a logarithmic double-phase operator in the framework of Musielak–Orlicz Sobolev spaces with variable exponents. Using the Galerkin approximation method and Young measure theory, we establish the existence of weak solutions under general and natural growth conditions on the nonlinear terms. Our approach extends the existing theory for variable exponent problems and provides a robust framework for studying nonhomogeneous and highly irregular diffusion phenomena in nonlinear analysis.