Front propagation for integro-differential KPP reaction–diffusion equations in periodic media

2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Panagiotis E. Souganidis ◽  
Andrei Tarfulea
Keyword(s):  
Reaction Diffusion ◽  
Front Propagation ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Periodic Media

scholarly journals Continuous dependence in front propagation of convective reaction-diffusion equations

2010 ◽  
Vol 9 (4) ◽  
pp. 1083-1098 ◽  
Author(s):  
Luisa Malaguti ◽  
◽  
Cristina Marcelli ◽  
Serena Matucci ◽  
◽  
...  
Keyword(s):  
Continuous Dependence ◽  
Reaction Diffusion ◽  
Front Propagation ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations

Front propagation for reaction–diffusion equations arising in combustion theory

1997 ◽  
Vol 14 (3) ◽  
pp. 277-292 ◽  
Author(s):  
G. Barles ◽  
C. Georgelin ◽  
P.E. Souganidis
Keyword(s):  
Reaction Diffusion ◽  
Front Propagation ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Combustion Theory

EXTERNAL NOISE AND FRONT PROPAGATION IN REACTION-TRANSPORT SYSTEMS WITH INERTIA: THE MEAN SPEED OF FISHER WAVES

2002 ◽  
Vol 02 (04) ◽  
pp. R109-R124 ◽  
Author(s):  
WERNER HORSTHEMKE
Keyword(s):  
Wave Speed ◽  
Reaction Diffusion ◽  
Front Propagation ◽  
External Noise ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Transport Systems ◽  
The Mean ◽  
Reaction Transport ◽  
Fisher Waves

We review the effect of spatiotemporal noise, white in time and colored in space, on front propagation in systems of reacting and dispersing particles, where the particle motion displays inertia or persistence. We discuss the three main approaches that have been developed to describe transport with inertia, namely hyperbolic reaction-diffusion equations, reaction-Cattaneo systems or reaction-telegraph equations, and reaction random walks. We focus on the mean speed of Fisher waves in these systems and study in particular reaction random walks, which are the most natural generalization of reaction-diffusion equations. Hyperbolic reaction-diffusion equations account for inertia in the transport process in an ad hoc way, whereas the other reaction-transport systems have a proper macroscopic or microscopic foundation. For the former, external noise affects neither the mean wave speed nor the region in parameter space for which Fisher waves exist. For the latter, external noise increases the mean wave speed of Fisher waves and decreases the upper limit for the characteristic time of the transport process, below which propagating fronts exist.

Convergence of front propagation for anisotropic bistable reaction–diffusion equations

1997 ◽  
Vol 15 (3-4) ◽  
pp. 325-358 ◽  
Author(s):  
Giovanni Bellettini ◽  
Piero Colli Franzone ◽  
Maurizio Paolini
Keyword(s):  
Reaction Diffusion ◽  
Front Propagation ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations
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