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Abstract <p>We prove the decay in time estimate of supremum norm of the nonnegative solution to the Cauchy problem for quasilinear degenerate parabolic equations with a gradient damping in Orlicz classes. Moreover, we give sufficient conditions on the behavior of the damping term which ensure the decay mass phenomena. In a certain sense, the results obtained cannot be improved: in the power case they coincide with the classical ones. Moreover, for Zygmund-type functions&#xa0;we obtain new critical exponents and new estimates of the stabilization rate of the solutions.</p>

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Behavior of the Solution to the Cauchy Problem for Degenerate Parabolic Equations with Gradient Damping in Orlicz Spaces

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Alexander F. Tedeev,
  • Anatoli F. Tedeev

摘要

Abstract

We prove the decay in time estimate of supremum norm of the nonnegative solution to the Cauchy problem for quasilinear degenerate parabolic equations with a gradient damping in Orlicz classes. Moreover, we give sufficient conditions on the behavior of the damping term which ensure the decay mass phenomena. In a certain sense, the results obtained cannot be improved: in the power case they coincide with the classical ones. Moreover, for Zygmund-type functions we obtain new critical exponents and new estimates of the stabilization rate of the solutions.