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<p>We investigate a class of anisotropic initial–boundary value problems involving the Finsler-Laplacian. Using a first-order differential inequality technique, we establish explicit conditions on the initial data that guarantee finite-time blow-up of solutions. Under alternative assumptions, a comparison principle yields global boundedness. Finally, employing a maximum principle for a suitable <i>P</i>-function in the sense of L.E. Payne, we derive explicit exponential time-decay estimates for the solution and its derivatives. The results extend classical isotropic theories to the anisotropic Finsler setting and contribute to the developing parabolic theory for such operators.</p>

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On the Asymptotic Behavior of the Solutions of a Class of Anisotropic Initial-Boundary Value Problems

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Cristian Enache,
  • Eylem Öztürk

摘要

We investigate a class of anisotropic initial–boundary value problems involving the Finsler-Laplacian. Using a first-order differential inequality technique, we establish explicit conditions on the initial data that guarantee finite-time blow-up of solutions. Under alternative assumptions, a comparison principle yields global boundedness. Finally, employing a maximum principle for a suitable P-function in the sense of L.E. Payne, we derive explicit exponential time-decay estimates for the solution and its derivatives. The results extend classical isotropic theories to the anisotropic Finsler setting and contribute to the developing parabolic theory for such operators.