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<p>This paper investigates the blow-up time for coupled parabolic equation systems with nonlinear boundary conditions. First, we prove that the solutions to these equations can blow-up within a finite time. Subsequently, by employing the auxiliary function method and modified differential inequality techniques,we derive upper and lower bounds of the blow-up time under specific conditions. To illustrate our findings and validate the theoretical framework, corresponding illustrative examples are provided.</p>

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Blow-up time analysis of coupled parabolic equation systems under nonlinear boundary conditions

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • Hongwei Liu,
  • Lingling Zhang,
  • Tao Liu

摘要

This paper investigates the blow-up time for coupled parabolic equation systems with nonlinear boundary conditions. First, we prove that the solutions to these equations can blow-up within a finite time. Subsequently, by employing the auxiliary function method and modified differential inequality techniques,we derive upper and lower bounds of the blow-up time under specific conditions. To illustrate our findings and validate the theoretical framework, corresponding illustrative examples are provided.