Global and non-global solutions to some chemotaxis model |
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Authors: | Hua Chen Junfeng Li Weian Liu |
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Institution: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China |
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Abstract: | The paper is concerned with some chemotaxis model ∂u/∂t=D▿(u▿ln(u/w))+u(a−bu),∂w/∂t=f(u,w). To study the behavior of the solution, some function transformations are introduced, and the main tool is sup-sub-solution
method. The result shows that, whether the solution blows up in finite time depends on the parameters and the initial data.
As the chemical substance w has linear growth, f(u,w)=βu−δw, where β>0, δ>0 and a+δ>0, wherein the solution exists globally. However, as w possesses exponential growth, f(u,w)=(βu−δ)w, wherein both u and w share the same blowup point and time if the solution blows up in finite time.
Biography: CHEN Hua(1956–), male, Professor, Ph. D., research direction: partial differential equation and its application. |
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Keywords: | chemotaxis blow up global solution sup-sub-solution |
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