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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

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