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<p>In this paper we study a haptotaxis and diffusion model of cancer invasion. The model consists of a parabolic PDE coupled with an ODE. The PDE itself contains the gradients of both unknowns, as well as well as the potential to be degenerate. This degeneracy appearing in the PDE provides the main source of difficulty for this system. We derive new estimates showing solutions must be bounded which then enable us to prove the global existence of weak solutions.</p>

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The Global Existence of Bounded Weak Solutions to a Degenerate Haptotaxis and Diffusion Model of Cancer Invasion

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • B. Price,
  • X. Xu

摘要

In this paper we study a haptotaxis and diffusion model of cancer invasion. The model consists of a parabolic PDE coupled with an ODE. The PDE itself contains the gradients of both unknowns, as well as well as the potential to be degenerate. This degeneracy appearing in the PDE provides the main source of difficulty for this system. We derive new estimates showing solutions must be bounded which then enable us to prove the global existence of weak solutions.