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Displaying similar documents to “On the speed of spread for fractional reaction-diffusion equations.”

Speed-up of reaction-diffusion fronts by a line of fast diffusion

Henri Berestycki, Anne-Charline Coulon, Jean-Michel Roquejoffre, Luca Rossi (2013-2014)

Séminaire Laurent Schwartz — EDP et applications

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In these notes, we discuss a new model, proposed by H. Berestycki, J.-M. Roquejoffre and L. Rossi, to describe biological invasions in the plane when a strong diffusion takes place on a line. This model seems relevant to account for the effects of roads on the spreading of invasive species. In what follows, the diffusion on the line will either be modelled by the Laplacian operator, or the fractional Laplacian of order less than 1. Of interest to us is the asymptotic speed of spreading...

Anomalous diffusion phenomena: A kinetic approach

Antoine Mellet (2014-2015)

Séminaire Laurent Schwartz — EDP et applications

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In this talk, we review some aspects of the derivation of fractional diffusion equations from kinetic equations and in particular some applications to the description of anomalous energy transport in FPU chains. This is based on joint works with N. Ben Abdallah, L. Cesbron, S. Merino, S. Mischler, C. Mouhot and M. Puel

Nonlinear Time-Fractional Differential Equations in Combustion Science

Pagnini, Gianni (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 34A08 (main), 34G20, 80A25 The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar...

Travelling Waves in Partially Degenerate Reaction-Diffusion Systems

B. Kazmierczak, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

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We study the existence and some properties of travelling waves in partially degenerate reaction-diffusion systems. Such systems may for example describe intracellular calcium dynamics in the presence of immobile buffers. In order to prove the wave existence, we first consider the non degenerate case and then pass to the limit as some of the diffusion coefficient converge to zero. The passage to the limit is based on a priori estimates of solutions independent of the values of the diffusion...

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method

Daftardar-Gejji, Varsha, Bhalekar, Sachin (2008)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 31B10 In the present paper a New Iterative Method [1] has been employed to find solutions of linear and non-linear fractional diffusion-wave equations. Illustrative examples are solved to demonstrate the efficiency of the method. * This work has partially been supported by the grant F. No. 31-82/2005(SR) from the University Grants Commission, N. Delhi, India.