The Influence of Fractional Diffusion in Fisher-KPP Equations

Communications in Mathematical Physics

Volumn 320, Issue 3, 2013, Pages 679-722

  Cabré, Xavier ^a   Roquejoffre, Jean Michel ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84878313652     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-013-1682-5     Document Type: Article

References (18)

1. Aronson D. G., Weinberger H. F.: Multidimensional nonlinear diffusion arising in population genetics. Adv. Math. 30, 33-76 (1978).
2. Berestycki H., Roquejoffre J.-M., Rossi L.: The periodic patch model for population dynamics with fractional diffusion. Disc. Cont. Dyn. Syst. Ser. S 4, 1-13 (2011).
3. Bony J.-M., Courrège P., Priouret P.: Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum. Ann. Inst. Fourier 18, 369-521 (1968).
4. Bramson, M.: Convergence of solutions of the Kolmogorov equation to travelling waves. Memoirs of the AMS 44, Providence, RI: Amer. Math. Soc., 1983.
5. Cabré X., Roquejoffre J.-M.: Propagation de fronts dans les équations de Fisher-KPP avec diffusion fractionnaire. C. R. Acad. Sci. Paris 347, 1361-1366 (2009).
6. Cazenave, T., Haraux, A.: An Introduction to Semilinear Evolution Equations. Oxford Lecture Series in Mathematics and its Applications 13. New York: Oxford University Press, 1998.
7. Del-Castillo-Negrete D., Carreras B. A., Lynch V. E.: Front propagation and segregation in a reaction-diffusion model with cross-diffusion. Phys. D 168/169, 45-60 (2002).
8. Del-Castillo-Negrete D., Carreras B. A., Lynch V. E.: Front Dynamics in Reaction-Diffusion Systems with Levy Flights: A Fractional Diffusion Approach. Phys. Rev. Lett. 91(1), 018302 (2003).
9. Engler, H.: On the speed of spread for fractional reaction-diffusion equations. Int. J. Diff. Eq. 2010 Art. ID 315421, 16 pp. (2010).
10. Garnier J.: Accelerating solutions in integro-differential equations. SIAM J. Math. Anal. 43, 1955-1974 (2011).
11. Hamel F., Roques L.: Fast propagation for KPP equations with slowly decaying initial conditions. J. Diff. Eqs. 249, 1726-1745 (2010).
12. Jones C. K. R. T.: Asymptotic behavior of a reaction-diffusion equation in higher space dimensions. Rocky Mountain J. Math. 13, 355-364 (1983).
13. Kolmogorov A. N., Petrovskii I. G., Piskunov N. S.: Etude de l'équation de diffusion avec accroissement de la quantité de matière, et son application à un problème biologique. Bjul. Moskowskogo Gos. Univ. 17, 1-26 (1937).
14. Kolokoltsov V. N.: Symmetric stable laws and stable-like jump-diffusions. London Math. Soc. 80, 725-768 (2000).
15. Lamperti J.: Semi-stable stochastic processes. Trans. Amer. Math. Soc. 104, 62-78 (1962).
16. Mancinelli R., Vergni D., Vulpiani A.: Front propagation in reactive systems with anomalous diffusion. Phys. D 185, 175-195 (2003).
17. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, 44. New York: Springer-Verlag, 1983.
18. Taira, K.: Diffusion Processes and Partial Differential Equations. Boston, MA: Academic Press, Inc., 1988.