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| The Pointwise Estimates of Solutions to the Cauchy Problem of a Chemotaxis Model |
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Citation： |
Renkun SHI,Weike WANG.The Pointwise Estimates of Solutions to the Cauchy Problem of a Chemotaxis Model[J].Chinese Annals of Mathematics B,2016,37(1):111~124 |
| Page view： 3472
Net amount： 1582 |
Authors： |
Renkun SHI; Weike WANG |
Foundation： |
The research of R. K. Shi was supported by the National
Natural Science Foundation of China (No.\,111 71213). The research
of W. K. Wang was supported by the National Natural Science
Foundation of China (No.\,11231006) and the National Research
Foundation for the Doctoral Program of Higher Education of China
(No.\,20130073110073) |
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| Abstract： |
This paper deals with an attraction-repulsion chemotaxis model (ARC)
in multi-dimensions. By Duhamel's principle, the implicit expression
of the solution to (ARC) is given. With the method of Green's
function, the authors obtain the pointwise estimates of solutions to
the Cauchy problem (ARC) for small initial data, which yield the
$W^{s,p}\ (1\le p\le\infty)$ decay properties of solutions. |
Keywords： |
Chemotaxis model, Pointwise estimates, Green's function, Decay rates |
Classification： |
35B40, 35Q80 |
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