Abstract
This paper concerns a parabolic-hyperbolic system on the half space R+ with boundary effect. The system is derived from a singular chemotaxis model describing the initiation of tumor angiogenesis. We show that the solution of the system subject to appropriate boundary conditions converges to a traveling wave profile as time tends to infinity if the initial data is a small perturbation around the wave which is shifted far away from the boundary but its amplitude can be arbitrarily large.
Original language | English |
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Pages (from-to) | 5168-5191 |
Number of pages | 24 |
Journal | Journal of Differential Equations |
Volume | 259 |
Issue number | 10 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
Keywords
- Asymptotic stability
- Boundary effect
- Chemotaxis
- Energy estimates
- Traveling wave solutions
ASJC Scopus subject areas
- Analysis