- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
8
2006
2
Travelling front solutions arising in the chemotaxis-growth model
Mitsuo
Funaki
Hiroshima National College of Maritime Technology, HIROSHIMA, JAPAN
Masayasu
Mimura
Meiji University, KAWASAKI, JAPAN
Tohru
Tsujikawa
Miyazaki University, MIYAZAKI, JAPAN
Chemotaxis, travelling front, singular perturbation, interfacial stability
We consider a bistable reaction-diffusion-advection system describing the growth of biological individuals which move by diffusion and chemotaxis. We use the singular limit procedure to study the dynamics of growth patterns arising in this system. It is shown that travelling front solutions are transversally stable when the chemotactic effect is weak and, when it becomes stronger, they are destabilized. Numerical simulations reveal that the destabilized solution evolves into complex patterns with dynamic network--like structures.
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
223
245
10.4171/IFB/141
http://www.ems-ph.org/doi/10.4171/IFB/141