Name
Title | ||
|---|---|---|
Large Time Behavior in a Multidimensional Chemotaxis-Haptotaxis Model with Slow Signal Diffusion |
Abstract | ||
|---|---|---|
This paper studies the coupled chemotaxis-haptotatxis system u(t) = Delta u-chi del.(u del v)-xi del.(u del w) + mu u(1 - u - w), x is an element of Omega, t > 0; v(t) = Delta v - v + u, x is an element of Omega, t > 0; w(t) = -vw, x is an element of Omega, t > 0, in a smoothly bounded domain Omega subset of R-n, n <= 3, with zero-flux boundary conditions, where chi, xi, and mu are given positive parameters. It is shown that whenever the initial data (u(0), v(0), w(0)) are nonnegative and suitably regular fulfilling u(0) 0 and w(0) <= 1, the third solution component w decays asymptotically in L-infinity(Omega). Moreover, under the fully explicit condition mu > chi(2)/8 the solution (u, v, w) exponentially stabilizes to the constant stationary solution (1, 1, 0) in the norm of L-infinity(Omega) as t -> infinity. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/15M1014115 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
chemotaxis,haptotaxis,logistic source,asymptotic stability | Mathematical optimization,Nabla symbol,Mathematical analysis,Stationary solution,Omega,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
47 | 6 | 0036-1410 |
Citations | PageRank | References |
3 | 0.82 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Youshan Tao | 1 | 22 | 7.04 |
| Michael Winkler | 2 | 23 | 5.52 |