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Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations
Joint Authors
Sánchez-Garduño, Faustino
Pérez-Velázquez, Judith
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-09-01
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D ( 0 ) = 0 ) and advection-degenerate (at h ′ ( 0 ) = 0 ) reaction-diffusion-advection (RDA) equation.
Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation.
We consider different forms of the convection term h ( u ) : ( 1 ) h ′ ( u ) is constant k , ( 2 ) h ′ ( u ) = k u with k > 0 , and ( 3 ) it is a quite general form which guarantees the degeneracy in the advective term.
In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0 , and then previous results reported from the authors can be extended.
For the other two cases, we use both analytical and numerical tools.
The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem.
This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates.
Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE.
American Psychological Association (APA)
Sánchez-Garduño, Faustino& Pérez-Velázquez, Judith. 2016. Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations. The Scientific World Journal،Vol. 2016, no. 2016, pp.1-21.
https://search.emarefa.net/detail/BIM-1120470
Modern Language Association (MLA)
Sánchez-Garduño, Faustino& Pérez-Velázquez, Judith. Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations. The Scientific World Journal No. 2016 (2016), pp.1-21.
https://search.emarefa.net/detail/BIM-1120470
American Medical Association (AMA)
Sánchez-Garduño, Faustino& Pérez-Velázquez, Judith. Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations. The Scientific World Journal. 2016. Vol. 2016, no. 2016, pp.1-21.
https://search.emarefa.net/detail/BIM-1120470
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1120470