Tohru Tsujikawa
University of Miyazaki
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Publication
Featured researches published by Tohru Tsujikawa.
Journal of The London Mathematical Society-second Series | 2006
Masashi Aida; Tohru Tsujikawa; Messoud Efendiev; Atsushi Yagi; Masayasu Mimura
This paper estimates from below the attractor dimension of the dynamical system determined from a chemotaxis growth model which was presented by Mimura and Tsujikawa. It is already known that the dynamical system has exponential attractors and it is also known by numerical computations that the model contains various pattern solutions. This paper is then devoted to estimating the attractor dimension from below and in fact to showing that, as the parameter of chemotaxis increases and tends to infinity, so does the attractor dimension. Such a result is in a good correlation with the numerical results.
Interfaces and Free Boundaries | 2006
Mitsuo Funaki; Masayasu Mimura; Tohru Tsujikawa
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.
Glasgow Mathematical Journal | 2009
Le Huy Chuan; Tohru Tsujikawa; Atsushi Yagi
We continue the study of a mathematical model for a forest ecosystem which has been presented by Y. A. Kuznetsov, M. Y. Antonovsky, V. N. Biktashev and A. Aponina (A cross-diffusion model of forest boundary dynamics, J. Math. Biol. 32 (1994), 219–232). In the preceding two papers (L. H. Chuan and A. Yagi, Dynamical systemfor forest kinematic model, Adv. Math. Sci. Appl. 16 (2006), 393– 409; L. H. Chuan, T. Tsujikawa and A. Yagi, Aysmptotic behavior of solutions for forest kinematic model, Funkcial. Ekvac. 49 (2006), 427–449), the present authors already constructed a dynamical system and investigated asymptotic behaviour of trajectories of the dynamical system. This paper is then devoted to studying not only the structure (including stability and instability) of homogeneous stationary solutions but also the existence of inhomogeneous stationary solutions. Especially it shall be shown that in some cases, one can construct an infinite number of discontinuous stationary solutions. 2000 Mathematics Subject Classification. 35J60, 37L15, 37N25.
Osaka Journal of Mathematics | 2006
Yasuhiro Takei; Messoud Efendiev; Tohru Tsujikawa; Atsushi Yagi
We improve our preceding result obtained in Tsujikawa and Ya gi [10]. We construct the similar exponential attractors to the same adsor bate-induced phase transition model as in [10] but in a convex domain by using the compac t smoothing property of corresponding nonlinear semigroup. In [10], the dom ain has been assumed to haveC3 regularity to ensure the squeezing property of semigroup.
Nonlinearity | 2013
Kousuke Kuto; Tohru Tsujikawa
This paper is concerned with stationary solutions of a reaction–diffusion-advection system arising in surface chemistry. Hildebrand et al (2003 New J. Phys. 5 61) have constructed stationary stripe (or spot) solutions of the system in the singular perturbation case and shown a numerical result that the set of stripe (or spot) solutions forms a saddle-node bifurcation curve with respect to a diffusion coefficient. In this paper, we introduce a shadow system in the limiting case that another diffusion and an advection coefficient tend to infinity. Furthermore we obtain the bifurcation structure of stationary solutions of the shadow systems in the one-dimensional case. This structure involves saddle-node bifurcation curves which support the above numerical result in Hildebrand et al (2003 New J. Phys. 5 61, figure 9). Our proof is based on the combination of the bifurcation, the singular perturbation and a level set analysis.
Archive | 2018
Tatsunari Sakurai; Tohru Tsujikawa; Daisuke Umeno
A concentric pulse by motile cells of Escherichia coli (E. coli) propagates and the cells aggregate to form self-organized patterns. We summarize experimental and numerical results on the self-organized pattern formation of E. coli to elucidate some aspects of its mechanism. Our presentation includes experiments on E. coli patterns, as well as numerical simulations on the basis of a reaction-diffusion-chemotaxis model. We find good agreement for one-dimensional propagating fronts in observation and simulation. However, corresponding results for two-dimensional circular bacterial clusters have still not been obtained.
Nonlinear Analysis-theory Methods & Applications | 2002
Koichi Osaki; Tohru Tsujikawa; Atsushi Yagi; Masayasu Mimura
Physica D: Nonlinear Phenomena | 2012
Kousuke Kuto; Koichi Osaki; Tatsunari Sakurai; Tohru Tsujikawa
Nonlinear Analysis-real World Applications | 2005
Masashi Aida; Koichi Osaki; Tohru Tsujikawa; Atsushi Yagi; Masayasu Mimura
Funkcialaj Ekvacioj-serio Internacia | 2006
Le Huy Chuan; Tohru Tsujikawa; Atsushi Yagi