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May  2010, 27(2): 827-846. doi: 10.3934/dcds.2010.27.827

Front propagation problems with sub-diffusion

1. 

Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

2. 

Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208-3125, United States

3. 

Department of Mathematics and Minerva Center for Nonlinear Physics of Complex Systems, Technion - Israel Institute of Technology, Haifa 32000, Israel

Received  October 2009 Revised  February 2010 Published  February 2010

Front propagation is considered for two kinds of sub-diffusion - reaction systems: (i) systems with sub-diffusion limited reaction rate governed by models with fractional time derivatives; (ii) systems with activation limited reaction rate governed by integro-differential equations with two time variables. It is shown that in the former case the front is described by a travelling wave solution, while in the latter the velocity of the front decreases with time.
Citation: Yana Nec, Vladimir A Volpert, Alexander A Nepomnyashchy. Front propagation problems with sub-diffusion. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 827-846. doi: 10.3934/dcds.2010.27.827
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