Journal article
Travelling wave solutions of the degenerate Kolmogorov–Petrovski–Piskunov equation
European journal of applied mathematics, v 14(3), pp 343-367
Jun 2003
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Abstract
We prove the existence of a family of Travelling Wave (TW) solutions for a large class of scalar reaction-diffusion equations with degenerate, nonlinear diffusion coefficients and monostable nonlinear reaction terms. We also investigate stability. Specifically, we show that, as in the linear diffusion case [6], the slowest TW in the family yields the asymptotic rate of the propagation of disturbances from the unstable rest state in these systems. In addition, we give conditions on the reaction term and diffusion coefficient ensuring the existence of interfaces.
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Details
- Title
- Travelling wave solutions of the degenerate Kolmogorov–Petrovski–Piskunov equation
- Creators
- G. S. Medvedev - Institute for Advanced StudyK. Ono - Boston UniversityP. J. Holmes - Princeton University
- Publication Details
- European journal of applied mathematics, v 14(3), pp 343-367
- Publisher
- Cambridge University Press
- Number of pages
- 25
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000184720000005
- Scopus ID
- 2-s2.0-0043133850
- Other Identifier
- 991021862734404721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied