Differential and Integral Equations

Simultaneous blowup and mass separation during collapse in an interacting system of chemotactic species

Elio Eduardo Espejo, Angela Stevens, and Takashi Suzuki

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Abstract

We study an interacting system of chemotactic species in two space dimensions. First, we show that there is a parameter region which ensures simultaneous blowup also for non-radially symmetric solutions. If the existence time of the solution is finite, there is a formation of collapse (possibly degenerate) for each component, total mass quantization, and formation of subcollapses. For radially symmetric solutions we can rigorously prove that the collapse concentrates mass on one component if the total masses of the other components are relatively small. Several related results are also shown.

Article information

Source
Differential Integral Equations, Volume 25, Number 3/4 (2012), 251-288.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012736

Mathematical Reviews number (MathSciNet)
MR2917884

Zentralblatt MATH identifier
1265.35135

Subjects
Primary: 35K55: Nonlinear parabolic equations 92C17: Cell movement (chemotaxis, etc.)

Citation

Espejo, Elio Eduardo; Stevens, Angela; Suzuki, Takashi. Simultaneous blowup and mass separation during collapse in an interacting system of chemotactic species. Differential Integral Equations 25 (2012), no. 3/4, 251--288. https://projecteuclid.org/euclid.die/1356012736


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