Nonlinear Analysis Real World Applications· 2026Q1
A free boundary analysis of tumor invasion driven by angiogenesis
- 1citations
- Q1SCImago
- 2026year
Short summary
A free boundary model demonstrates that tumors, once formed, maintain positive thickness and invade host tissue exponentially when cell spreading (κ) is high, or remain bounded/contract when κ is low.
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Key points
- A free boundary model captures tumor invasion driven by diffusion, chemotaxis, and angiogenesis.
- Tumors are proven to survive through time, maintaining strictly positive thickness.
- Two invasion regimes are identified based on the ratio κ: exponential growth for high κ, and bounded/contracting for low κ.
- An explicit expression for tumor evolution is derived from initial data.
AI-generated from the title and abstract; the full text is not read.
Abstract
We discuss a free boundary model for tumor invasion that describes a cloud of cells that diffuse and, at the same time, are drifted along the vector field of the chemotactic direction. The model captures the evolution of a solid tumor, including the process of angiogenesis, which consists in the formation of new blood vessels that supply the tumor with oxygen and other nutrients, thereby promoting its spread and growth. We prove that, once formed, the tumor survives through time, maintaining strictly positive thickness. An explicit expression in terms of the initial data is derived. Moreover, we distinguish two regimes depending on the ratio κ between the spreading of tumor cells and the growth of the tumor mass. If κ is sufficiently large, then the tumor grows exponentially in time and invades the entire host tissue. In contrast, if κ is small enough, then either the tumor remains bounded in size over time or may experience a fast contraction.
The authors' abstract, as published at the source. Nonlinear Analysis Real World Applications, 2026 · DOI ↗
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Field: Modeling and Simulation
Modeling and SimulationMathematics