Preprint 52/1998

Steady state solutions of a reaction-diffusion system modeling chemotaxis

Guofang Wang and Jun-Cheng Wei

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Submission date: 16. Nov. 1998
Pages: 21
published in: Mathematische Nachrichten, 233/234 (2002), p. 221-236 
Bibtex

Abstract:
We study the following nonlinear elliptic equation
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where tex2html_wrap_inline24 is a smooth bounded domain in tex2html_wrap_inline26. This equation arises in the study of stationary solutions of a chemotaxis system proposed by Keller and Segel. Under the condition that tex2html_wrap_inline28 for m=1,2,..., where tex2html_wrap_inline32 is the first (nonzero) eigenvalue of tex2html_wrap_inline34 under the Neumann boundary condition, we establish the existence of a solution to the above equation. Our idea is a combination of Struwe's technique and blow up analysis for a problem with Neumann boundary condition.

23.06.2018, 02:10