Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T01:10:50.333Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite travelling waves for semilinear parabolic systems

Published online by Cambridge University Press:  20 January 2009

Ming-Xin Wang
Ming-Xin Wang
Affiliation:
Department of Applied Mathematics, Southeast University, Nanjing 210018, P.R. China E-mail address: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, finite travelling waves for the semilinear parabolic systems

are studied, where di > 0, ei > 0, mij ≥ 0 for all 1 ≤ i,j ≤ n, and for all 1 ≤ i ≤ n. Let M = (mij)n × n and A = I – M. It will be proved that (*) has finite travelling waves if and only if all principal minors of A are positive. Moreover, some asymptotic behaviours of finite travelling waves will be obtained.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 83 - 93
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Berman, A. and Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences (Academic Press, New York, 1979).Google Scholar
2.Esquinas, J. and Herrero, M. A., Travelling wave solutions to semilinear diffusion system, SIAM J. Math. Anal. 21 (1990), 123–136.Google Scholar
3.Ladde, G. S., Lakshmikantham, V. and Vatsala, V. S., Monotone Iterative Techniques for Nonlinear Differential Equations (Pitman, New York, 1985).Google Scholar
4.Walter, W., Differential and Integral Inequalities (Springer-Verlag, 1970).Google Scholar
5.Wang, M. X., Existence of finite travelling waves for a nonlinear parabolic system, Nonlinear Anal., TMA 22 (1994), 1487–1500.CrossRefGoogle Scholar
6.Wang, M. X., Nonlinear Equations of Parabolic Type (Science Press, Beijing, 1993), in Chinese.Google Scholar