Geodesic
Travelling front solutions arising in the chemotaxis-growth model
Mitsuo Funaki1 ; Masayasu Mimura2 ; Tohru Tsujikawa3
1Hiroshima National College of Maritime Technology, Japan
2Meiji University, Kawasaki, Japan
3Miyazaki University, Japan
Interfaces and free boundaries, Tome 8 (2006) no. 2, pp. 223-245

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DOI

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.
DOI : 10.4171/ifb/141
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Chemotaxis, travelling front, singular perturbation, interfacial stability

Mitsuo Funaki  1   ; Masayasu Mimura  2   ; Tohru Tsujikawa  3

1 Hiroshima National College of Maritime Technology, Japan
2 Meiji University, Kawasaki, Japan
3 Miyazaki University, Japan 
Mitsuo Funaki; Masayasu Mimura; Tohru Tsujikawa. Travelling front solutions arising in the chemotaxis-growth model. Interfaces and free boundaries, Tome 8 (2006) no. 2, pp. 223-245. doi: 10.4171/ifb/141
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     title = {Travelling front solutions arising in the chemotaxis-growth model},
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     pages = {223--245},
     year = {2006},
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     number = {2},
     doi = {10.4171/ifb/141},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/141/}
}
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