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Local existence and uniqueness of solutions to one-dimensional tumor invasion model
In the present paper, we propose a modified tumor invasion model which was originally proposed in Chaplain and Anderson (2003) . And we show the local existence and uniqueness of solutions to approximate systems of ...
The Neumann problem in an irregular domain
(EMS, Interfaces and Free Boundaries, 2010)
We consider the stability of patterns for the reaction-diffusion equation with Neumann boundary conditions in an irregular domain in ℝN, N ≥ 2, the model example being two convex regions connected by a small ‘hole’ in their ...
Simulating Phase Transition Dynamics on Non-trivial Domains
(Lecture Notes in Computer Science, 2013)
Our goal is to investigate the influence of the geometry and topology of the domain Ω on the solutions of the phase transition and other diffusion-driven phenomena in Ω, modeled e.g. by the Allen-Cahn, Cahn-Hilliard, ...