On the Speed of Spread for Fractional Reaction-Diffusion Equations
Author
Source
International Journal of Differential Equations
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-11-19
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
The fractional reaction diffusion equation ∂tu+Au=g(u) is discussed, where A is a fractional differential operator on ℝ of order α∈(0,2), the C1 function g vanishes at ζ=0 and ζ=1, and either g≥0 on (0,1) or g<0 near ζ=0.
In the case of nonnegative g, it is shown that solutions with initial support on the positive half axis spread into the left half axis with unbounded speed if g(ζ) satisfies some weak growth condition near ζ=0 in the case α>1, or if g is merely positive on a sufficiently large interval near ζ=1 in the case α<1.
On the other hand, it shown that solutions spread with finite speed if g′(0)<0.
The proofs use comparison arguments and a suitable family of travelling wave solutions.
American Psychological Association (APA)
Engler, Hans. 2009. On the Speed of Spread for Fractional Reaction-Diffusion Equations. International Journal of Differential Equations،Vol. 2010, no. 2010, pp.1-16.
https://search.emarefa.net/detail/BIM-462810
Modern Language Association (MLA)
Engler, Hans. On the Speed of Spread for Fractional Reaction-Diffusion Equations. International Journal of Differential Equations No. 2010 (2010), pp.1-16.
https://search.emarefa.net/detail/BIM-462810
American Medical Association (AMA)
Engler, Hans. On the Speed of Spread for Fractional Reaction-Diffusion Equations. International Journal of Differential Equations. 2009. Vol. 2010, no. 2010, pp.1-16.
https://search.emarefa.net/detail/BIM-462810
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-462810