Journal article
LARGE-TIME BEHAVIOR OF A PARABOLIC-PARABOLIC CHEMOTAXIS MODEL WITH LOGARITHMIC SENSITIVITY IN ONE DIMENSION
Discrete and continuous dynamical systems. Series B, Vol.18(3), pp.821-845
05/01/2013
DOI: 10.3934/dcdsb.2013.18.821
Abstract
This paper deals with the chemotaxis system
{u(t) = Du(xx) - chi[u(ln v)(x)](x), x is an element of (0, 1), t > 0,
v(t) = epsilon v(xx) + uv - mu v, x is an element of (0, 1), t > 0,
under Neumann boundary condition, where chi < 0, D > 0, epsilon > 0 and mu > 0 are constants.
It is shown that for any sufficiently smooth initial data (u(0), v(0)) fulfilling u(0) >= 0, u(0) not equivalent to 0 and v(0) > 0, the system possesses a unique global smooth solution that enjoys exponential convergence properties in L-infinity(Omega) as time goes to infinity, which depend on the sign of mu - (u) over bar (0), where (u) over bar (0) := integral(1)(0) u0dx. Moreover, we prove that the constant pair (mu, (mu/lambda)(D/chi)) (where lambda > 0 is an arbitrary constant) is the only positive stationary solution. The biological implications of our results will be given in the paper.
Details
- Title: Subtitle
- LARGE-TIME BEHAVIOR OF A PARABOLIC-PARABOLIC CHEMOTAXIS MODEL WITH LOGARITHMIC SENSITIVITY IN ONE DIMENSION
- Creators
- Youshan Tao - Donghua UniversityLihe Wang - University of IowaZhi-An Wang - Hong Kong Polytechnic University
- Resource Type
- Journal article
- Publication Details
- Discrete and continuous dynamical systems. Series B, Vol.18(3), pp.821-845
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- DOI
- 10.3934/dcdsb.2013.18.821
- ISSN
- 1531-3492
- eISSN
- 1553-524X
- Number of pages
- 25
- Grant note
- 11171061 / National Natural Science Foundation of China 502711 / Hong Kong RGC general research fund 13ZZ046 / Innovation Program of Shanghai Municipal Education Commission
- Language
- English
- Date published
- 05/01/2013
- Academic Unit
- Mathematics
- Record Identifier
- 9984240764702771
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