Advanced Studies in Pure Mathematics

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

Takao Ohta

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

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

Permanent link to this document euclid.aspm/1540934209

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

Export citation