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STATIONARY SOLUTIONS TO FOREST KINEMATIC MODEL

Published online by Cambridge University Press:  01 January 2009

LE HUY CHUAN ,
TOHRU TSUJIKAWA  and
ATSUSHI YAGI
LE HUY CHUAN
Affiliation:
Department of Environmental Technology, Osaka University, Suita, Osaka 565-0871, Japan e-mail: chuanlh@ap.eng.osaka-u.ac.jp
TOHRU TSUJIKAWA
Affiliation:
Faculty of Engineering, Miyazaki University, Miyazaki 889-2192, Japan e-mail: tujikawa@cc.miyazaki-u.ac.jp
ATSUSHI YAGI*
Affiliation:
Department of Applied Physics, Osaka University, Suita, Osaka 565-0871, Japan e-mail: yagi@ap.eng.osaka-u.ac.jp
*
*Corresponding author.
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Abstract

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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.

Keywords

35J6037L1537N25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 1 , January 2009 , pp. 1 - 17
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Aida, M., Tsujikawa, T., Efendiev, M., Yagi, A. and Mimura, M., Lower estimate of attractor dimension for chemotaxis growth system, J. Lond. Math. Soc. 74 (2006), 453–474.CrossRefGoogle Scholar
2.Antonovsky, M. Y., Impact of the factors of the environment on the dynamics of population (mathematical models), in Proceedings of Soviet-American Symposium “Comprehensive Analysis of the Environment”, Tbilisi 1974, Leningrad: Hydromet (1975), 218–230.Google Scholar
3.Antonovsky, M. Y. and Korzukhin, M. D., Mathematical modeling of economic and ecological-economic process, in Proceedings of International Symposium “Integrated Global Monitoring of Environmental Pollution”, Tbilisi 1981, Leningrad: Hydromet (1983), 353–358.Google Scholar
4.Babin, A. V. and Vishik, M. I., Attractors of evolution equations (North-Holland, Amsterdam, 1992).Google Scholar
5.Botkin, D. B., Forest dynamics–an ecological model (Oxford University Press, Oxford, UK, 1993).Google Scholar
6.Botkin, D. B., Janak, J. F. and Wallis, J. R., Some ecological consequences of a computer model of forest growth, J. Ecol. 60 (1972), 849–872.CrossRefGoogle Scholar
7.Chuan, L. H. and Yagi, A., Dynamical system for forest kinematic model, Adv. Math. Sci. Appl. 16 (2006), 393–409.Google Scholar
8.Chuan, L. H., Tsujikawa, T. and Yagi, A., Asymptotic behavior of solutions for forest kinematic model, Funkcial. Ekvac. 49 (2006), 427–449.CrossRefGoogle Scholar
9.Dautray, R. and Lions, J. L., Mathematical analysis and numerical methods for science and technology, Vol. 2 (Springer-Verlag, Berlin, 1988).Google Scholar
10.Grisvard, P., Elliptic problems in nonsmooth domains (Pitman, London, 1985).Google Scholar
11.Kuznetsov, Y. A., Antonovsky, M. Y., Biktashev, V. N. and Aponina, A., A cross-diffusion model of forest boundary dynamics, J. Math. Biol. 32 (1994), 219–232.CrossRefGoogle Scholar
12.Nakaguchi, E. and Yagi, A., Fully discrete approximation by Galerkin Runge–Kutta methods for quasilinear parabolic systems, Hokkaido Math. J. 31 (2002), 385–429.CrossRefGoogle Scholar
13.Nakata, H., Numerical simulations for forest boundary dynamics model, Masters thesis (Osaka University, 2004).Google Scholar
14.Osaki, K. and Yagi, A., Global existence for a chemotaxis-growth system in ℝ2, Adv. Math. Sci. Appl. 12 (2002), 587–606.Google Scholar
15.Pacala, S. W., Canham, C. D. and Saponara, J., Forest models defined by fields measurements: estimation, error analysis and dynamics, Ecol. Monogr. 66 (1996), 1–43.CrossRefGoogle Scholar
16.Pacala, S. W. and Deutchman, D. H., Details that matter: the spatial distribution of individual trees maintains forest ecosystem functions, Oikos 74 (1995), 357–365.CrossRefGoogle Scholar
17.Temam, R., Infinite-dimensional dynamical systems in mechanics and physics, 2nd ed. (Springer-Verlag, Berlin, 1997).CrossRefGoogle Scholar
18.Triebel, H., Interpolation theory, function spaces, differential operators (North-Holland, Amsterdam, 1978).Google Scholar
19.Wells, J. C., Invariant manifolds on non-linear operators, Pacific J. Math. 62 (1976), 285–293.CrossRefGoogle Scholar