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2010 On the Speed of Spread for Fractional Reaction-Diffusion Equations
Hans Engler
Int. J. Differ. Equ. 2010(SI1): 1-16 (2010). DOI: 10.1155/2010/315421


The fractional reaction diffusion equation tu+Au=g(u) is discussed, where A is a fractional differential operator on of order α(0,2), the C1 function g vanishes at ζ=0 and ζ=1, and either g0 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.


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Hans Engler. "On the Speed of Spread for Fractional Reaction-Diffusion Equations." Int. J. Differ. Equ. 2010 (SI1) 1 - 16, 2010.


Received: 12 August 2009; Revised: 12 October 2009; Accepted: 25 October 2009; Published: 2010
First available in Project Euclid: 26 January 2017

zbMATH: 1225.35252
MathSciNet: MR2564004
Digital Object Identifier: 10.1155/2010/315421

Rights: Copyright © 2010 Hindawi

Vol.2010 • No. SI1 • 2010
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