Differential and Integral Equations

A priori bounds of stationary solutions of two dimensional Keller-Segel system on polygonal domains

Yoshifumi Mimura

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Abstract

We consider a Neumann boundary problem like Gelfand's problem on polygonal domains and prove that a priori bounds of solutions fail for specific parameters. The same results are already proved by Senba-Suzuki in 2000 when domains are open sets in $\mathbb{R}^2$ with smooth boundaries. The novelty is that the foregoing specific parameters depend on angles of polygonal domains.

Article information

Source
Differential Integral Equations, Volume 28, Number 3/4 (2015), 347-360.

Dates
First available in Project Euclid: 4 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1423055232

Mathematical Reviews number (MathSciNet)
MR3306567

Zentralblatt MATH identifier
1340.35050

Subjects
Primary: 35B45: A priori estimates 35J25: Boundary value problems for second-order elliptic equations 35J60: Nonlinear elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations

Citation

Mimura, Yoshifumi. A priori bounds of stationary solutions of two dimensional Keller-Segel system on polygonal domains. Differential Integral Equations 28 (2015), no. 3/4, 347--360. https://projecteuclid.org/euclid.die/1423055232


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