Advanced Studies in Pure Mathematics

Self-propelled dynamics of deformable domain in excitable reaction diffusion systems

Takao Ohta

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Abstract

The time-evolution equations for an isolated domain in an excitable reaction-diffusion system are derived both in two and three dimensions by an interfacial approach near the drift bifurcation where a motionless state becomes unstable and a domain starts propagation at a certain velocity. The coupling between shape deformation of domain and the migration velocity is taken into consideration. When the relaxation of shape deformation is slow enough, a straight motion becomes unstable and several kinds of motion of domain appear depending on the parameters. The self-propelled domain dynamics under the external fields is also studied.

Article information

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 137-149

Dates
Received: 8 January 2012
Revised: 4 February 2013
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934209

Digital Object Identifier
doi:10.2969/aspm/06410137

Mathematical Reviews number (MathSciNet)
MR3381198

Zentralblatt MATH identifier
1336.35199

Subjects
Primary: 37L05: General theory, nonlinear semigroups, evolution equations 70K50: Bifurcations and instability 92C10: Biomechanics [See also 74L15]

Keywords
Excitable reaction-diffusion system drift bifurcation interfacial approach self-propelled motion

Citation

Ohta, Takao. Self-propelled dynamics of deformable domain in excitable reaction diffusion systems. Nonlinear Dynamics in Partial Differential Equations, 137--149, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410137. https://projecteuclid.org/euclid.aspm/1540934209


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