Abstract
We generalize the one-dimensional population model of Anguige & Schmeiser [1] reflecting the cell-to-cell adhesion and volume filling and classify the resulting equation into the six types. Among these types, we fix one that yields a class of advection-diffusion equations of forward-backward-forward type and prove the existence of infinitely many global-in-time weak solutions to the initial-Dirichlet boundary value problem when the maximum value of an initial population density exceeds a certain threshold. Such solutions are extracted from the method of convex integration by Müller & Šverák [12]; they exhibit fine-scale density mixtures over a finite time interval, then become smooth and identical, and decay exponentially and uniformly to zero as time approaches infinity. TE check: Please check the reference citation in abstract.
Original language | English |
---|---|
Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
DOIs | |
State | Accepted/In press - 2024 |
Keywords
- adhesion and volume filling
- convex integration
- forward-backward-forward type
- partial differential inclusion
- Population model