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Existence of Alternate Steady States in a Phosphorous Cycling Model
Joint Authors
Shivaji, R.
Butler, Dagny
Sasi, Sarath
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-14
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We analyze the positive solutions to the steady-state reaction diffusion equation with Dirichlet boundary conditions of the form: -Δu=λ[K-u+c(u4/(1+u4))], x∈Ω, u=0, x∈∂Ω.
Here, Δu=div(∇u) is the Laplacian of u, 1/λ is the diffusion coefficient, K and c are positive constants, and Ω⊂RN is a smooth bounded region with ∂Ω in C2.
This model describes the steady states of phosphorus cycling in stratified lakes.
Also, it describes the colonization of barren soils in drylands by vegetation.
In this paper, we discuss the existence of multiple positive solutions leading to the occurrence of an S-shaped bifurcation curve.
We prove our results by the method of subsuper solutions.
American Psychological Association (APA)
Butler, Dagny& Sasi, Sarath& Shivaji, R.. 2012. Existence of Alternate Steady States in a Phosphorous Cycling Model. ISRN Mathematical Analysis،Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-504806
Modern Language Association (MLA)
Butler, Dagny…[et al.]. Existence of Alternate Steady States in a Phosphorous Cycling Model. ISRN Mathematical Analysis No. 2012 (2012), pp.1-11.
https://search.emarefa.net/detail/BIM-504806
American Medical Association (AMA)
Butler, Dagny& Sasi, Sarath& Shivaji, R.. Existence of Alternate Steady States in a Phosphorous Cycling Model. ISRN Mathematical Analysis. 2012. Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-504806
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-504806