Details
| Original language | English |
|---|---|
| Pages (from-to) | 1564-1595 |
| Number of pages | 32 |
| Journal | NONLINEARITY |
| Volume | 29 |
| Issue number | 5 |
| Publication status | Published - 29 Mar 2016 |
| Externally published | Yes |
Abstract
This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion. (Equation presented) under homogeneous Neumann boundary conditions in a bounded smooth domain Ω ∪-ℝn, n=2,3,4, where χ, -ζ and μ are given nonnegative parameters. The diffusivity D(u) is assumed to satisfy D(u) ≥ δμm-1 for all u > 0 with some δ > 0. It is proved that for sufficiently regular initial data global bounded solutions exist whenever m > 2-2/n. For the case of non-degenerate diffusion (i.e. D(0) > 0) the solutions are classical; for the case of possibly degenerate diffusion (D(0) ≥ 0), the existence of bounded weak solutions is shown.
Keywords
- Boundedness, Chemotaxis, Global existence, Haptotaxis, Partial differential equations
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- General Physics and Astronomy
- Mathematics(all)
- Applied Mathematics
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In: NONLINEARITY, Vol. 29, No. 5, 29.03.2016, p. 1564-1595.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Boundedness in a chemotaxis-haptotaxis model with nonlinear diffusion
AU - Li, Yan
AU - Lankeit, Johannes
N1 - Funding Information: The fist author has been supported by China Scholarship Council (No.201406090072) and in part by National Natural Science Foundation of China (No.11171063).
PY - 2016/3/29
Y1 - 2016/3/29
N2 - This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion. (Equation presented) under homogeneous Neumann boundary conditions in a bounded smooth domain Ω ∪-ℝn, n=2,3,4, where χ, -ζ and μ are given nonnegative parameters. The diffusivity D(u) is assumed to satisfy D(u) ≥ δμm-1 for all u > 0 with some δ > 0. It is proved that for sufficiently regular initial data global bounded solutions exist whenever m > 2-2/n. For the case of non-degenerate diffusion (i.e. D(0) > 0) the solutions are classical; for the case of possibly degenerate diffusion (D(0) ≥ 0), the existence of bounded weak solutions is shown.
AB - This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion. (Equation presented) under homogeneous Neumann boundary conditions in a bounded smooth domain Ω ∪-ℝn, n=2,3,4, where χ, -ζ and μ are given nonnegative parameters. The diffusivity D(u) is assumed to satisfy D(u) ≥ δμm-1 for all u > 0 with some δ > 0. It is proved that for sufficiently regular initial data global bounded solutions exist whenever m > 2-2/n. For the case of non-degenerate diffusion (i.e. D(0) > 0) the solutions are classical; for the case of possibly degenerate diffusion (D(0) ≥ 0), the existence of bounded weak solutions is shown.
KW - Boundedness
KW - Chemotaxis
KW - Global existence
KW - Haptotaxis
KW - Partial differential equations
UR - http://www.scopus.com/inward/record.url?scp=84966393250&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1508.05846
DO - 10.48550/arXiv.1508.05846
M3 - Article
AN - SCOPUS:84966393250
VL - 29
SP - 1564
EP - 1595
JO - NONLINEARITY
JF - NONLINEARITY
SN - 0951-7715
IS - 5
ER -