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We consider a generalized form of the Cahn–Hilliard equation, supplied with Neumann boundary conditions. This problem describes the growth of cancerous cells. We proved that the (biological) solution does not exist in general and it can blow up in a finite time. In such cases, we proved the global existence of a unique solution.

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Blow Up Solutions for a Variant of the Cahn–Hilliard Equation Describing Growth of Cancerous Cells

  • 会议论文

  • 发表日期：

    2025年

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  • Hussein Fakih,
  • Salam Abou Baraki,
  • Ragheb Mghames,
  • Yahia Awad

摘要

We consider a generalized form of the Cahn–Hilliard equation, supplied with Neumann boundary conditions. This problem describes the growth of cancerous cells. We proved that the (biological) solution does not exist in general and it can blow up in a finite time. In such cases, we proved the global existence of a unique solution.