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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 1
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Original Articles

Memory effects and random walks in reaction-transport systems

J. A. Ferreira Department of Mathematics, University of Coimbra, PortugalCorrespondence[email protected]
&
P. De Oliveira Department of Mathematics, University of Coimbra, Portugal
Pages 99-118 | Received 06 Mar 2006, Accepted 10 Nov 2006, Published online: 10 Apr 2007

References

  • Araújo , A , Ferreira , JA and Oliveira , P . 2005 . Qualitative behaviour of numerical traveling waves solutions for reaction diffusion equations with memory . Applicable Analysis , 84 : 1231 – 1246 .
  • Araújo , A , Ferreira , JA and Oliveira , P . 2006 . The effect of memory terms in the qualitative behaviour of the solution of diffusion equations . Journal of Computational Mathematics , 24 : 91 – 102 .
  • Aronson , DG and Weinberger , HF . 1978 . Multidimensional nonlinear diffusion in population genetics . Advanced Mathematics , 30 : 33 – 76 .
  • Branco , JR , Ferreira , JA and Oliveira , P . Numerical methods for generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation . Applied Numerical Mathematics , (To appear)
  • Debnath , L . 1997 . Nonlinear Partial Differential Equations for Scientists and Engineers , Boston : Birkhuser .
  • Fedotov , S . 1998 . Traveling waves in a reaction – diffusion system: diffusion with finite velocity and Kolmogorov–Petrovski–Piskunov kinectics . Physical Review E , 5 ( 4 ) : 5143 – 5145 .
  • Fedotov , S . 1999 . Nonuniform reaction rate distribution for the generalized Fisher equation: ignition ahead of the reaction front . Physical Review E , 60 ( 4 ) : 4958 – 4961 .
  • Fedotov , S . 2001 . Front propagation into an unstable state of reaction – transport systems . Physical Review Letter , 86 ( 5 ) : 926 – 929 .
  • Fedotov , S and Okuda , Y . 2002 . Non Markovian random process and traveling front in a reaction transport system with memory and long-range interactions . Physical Review E , 66 : 021113 – 021119 .
  • Fedotov , S and Okuda , Y . 2004 . Waves in a reaction-transport system with memory, long-range interactions and transmutations . Physical Review E , 70 : 051108 – 051117 .
  • Fisher , RA . 1937 . The wave of advance of advantageous genes . Annals of Eugenics , 7 : 353 – 369 .
  • Kolmogorov , A , Petrovskii , I and Piskunov , N . 1937 . Étude de l'equation de la diffusion avec croissance de la matière et son application à un problème biologique. Moscow University . Bulletien Mathematics , 1 : 1 – 25 .
  • Mendez , V , Pujol , T and Fort , J . 2002 . Dispersal probability distributions and the wave-front speed problem . Physical Review E , 65 : 041109 – 041114 .
  • Zauderer , E . 1983 . Partial Differential Equations of Applied Mathematics , New York : John Wiley Sons .

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