-
Previous Article
Effective viscosity of bacterial suspensions: a three-dimensional PDE model with stochastic torque
- CPAA Home
- This Issue
-
Next Article
Preface
Sharp interface limit of the Fisher-KPP equation
1. | I3M, Université de Montpellier 2, CC051, Place Eugène Bataillon, 34095 Montpellier Cedex 5 |
2. | UMR CNRS 5251, I.M.B. and INRIA Bordeaux Sud-ouest Anubis, case 36, UFR Sciences et Modélisation, Université Victor Segalen Bordeaux 2, 3 ter, place de la Victoire - 33076 Bordeaux cedex |
References:
[1] |
M. Alfaro, D. Hilhorst and H. Matano, The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system,, J. Differential Equations, 245 (2008), 505. Google Scholar |
[2] |
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation,, Partial differential equations and related topics (Program, (1974), 5.
|
[3] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics,, Adv. Math., 30 (1978), 33.
|
[4] |
G. Barles, L. C. Evans and P. E. Souganidis, Wavefront propagation for reaction-diffusion systems of PDE,, Duke Math. J., 61 (1990), 835.
|
[5] |
G. Barles and P. E. Souganidis, A remark on the asymptotic behavior of the solution of the KPP equation,, C. R. Acad. Sci. Paris S\'er. I Math., 319 (1994), 679.
|
[6] |
H. Berestycki and F. Hamel, On the general definition of transition waves and their properties,, preprint., (). Google Scholar |
[7] |
H. Berestycki, F. Hamel and N. Nadirashvili, The speed of propagation for KPP type problems. II. General domains,, J. Amer. Math. Soc., 23 (2010), 1.
|
[8] |
H. Berestycki, F. Hamel and L. Roques, Équations de réaction-diffusion et modèles d'invasions biologiques dans les milieux périodiques,, C. R. Math. Acad. Sci. Paris, 339 (2004), 549.
|
[9] |
X. Chen, Generation and propagation of interfaces for reaction-diffusion equations,, J. Differential Equations, 96 (1992), 116.
|
[10] |
L. C. Evans and P. E. Souganidis, A PDE approach to geometric optics for certain semilinear parabolic equations,, Indiana Univ. Math. J., 38 (1989), 141.
|
[11] |
E. Feireisl, Front propagation for degenerate parabolic equations,, Nonlinear Anal., 35 (1999), 735.
|
[12] |
R. A. Fisher, The wave of advance of advantageous genes,, Ann. of Eugenics, 7 (1937), 355. Google Scholar |
[13] |
M. I. Freidlin, Limit theorems for large deviations and reaction-diffusion equations,, Ann. Probab., 13 (1985), 639.
|
[14] |
D. Hilhorst, R. Kersner, E. Logak and M. Mimura, Interface dynamics of the Fisher equation with degenerate diffusion,, J. Differential Equations, 244 (2008), 2872.
|
[15] |
A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Etude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique,, Bulletin Universit\'e d'Etat Moscou, (1937), 1. Google Scholar |
[16] |
H. Malchow, S. V. Petrovskii and E. Venturino, "Spatiotemporal Patterns in Ecology and Epidemiology. Theory, Models, and Simulations,", Mathematical and Computational Biology Series, (2008).
|
[17] |
S. V. Petrovskii and H. Malchow, eds. (2005), "Biological Invasions in a Mathematical Perspective,", (A special issue of Biological Invasions: Proceedings of Computational and Mathematical Population Dynamics, (2004), 21. Google Scholar |
[18] |
N. Shigesada and K. Kawasaki, "Biological Invasion: Theory and Practise,", Oxford University Press, (1997). Google Scholar |
[19] |
S. Vakulenko and V. Volpert, Generalized travelling waves for perturbed monotone reaction-diffusion systems,, Nonlinear Anal., 46 (2001), 757.
|
[20] |
A. Volpert, V. Volpert, V. Volpert, "Travelling Wave Solutions of Parabolic Systems,", Translations of Mathematical Monographs, (1994).
|
show all references
References:
[1] |
M. Alfaro, D. Hilhorst and H. Matano, The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system,, J. Differential Equations, 245 (2008), 505. Google Scholar |
[2] |
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation,, Partial differential equations and related topics (Program, (1974), 5.
|
[3] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics,, Adv. Math., 30 (1978), 33.
|
[4] |
G. Barles, L. C. Evans and P. E. Souganidis, Wavefront propagation for reaction-diffusion systems of PDE,, Duke Math. J., 61 (1990), 835.
|
[5] |
G. Barles and P. E. Souganidis, A remark on the asymptotic behavior of the solution of the KPP equation,, C. R. Acad. Sci. Paris S\'er. I Math., 319 (1994), 679.
|
[6] |
H. Berestycki and F. Hamel, On the general definition of transition waves and their properties,, preprint., (). Google Scholar |
[7] |
H. Berestycki, F. Hamel and N. Nadirashvili, The speed of propagation for KPP type problems. II. General domains,, J. Amer. Math. Soc., 23 (2010), 1.
|
[8] |
H. Berestycki, F. Hamel and L. Roques, Équations de réaction-diffusion et modèles d'invasions biologiques dans les milieux périodiques,, C. R. Math. Acad. Sci. Paris, 339 (2004), 549.
|
[9] |
X. Chen, Generation and propagation of interfaces for reaction-diffusion equations,, J. Differential Equations, 96 (1992), 116.
|
[10] |
L. C. Evans and P. E. Souganidis, A PDE approach to geometric optics for certain semilinear parabolic equations,, Indiana Univ. Math. J., 38 (1989), 141.
|
[11] |
E. Feireisl, Front propagation for degenerate parabolic equations,, Nonlinear Anal., 35 (1999), 735.
|
[12] |
R. A. Fisher, The wave of advance of advantageous genes,, Ann. of Eugenics, 7 (1937), 355. Google Scholar |
[13] |
M. I. Freidlin, Limit theorems for large deviations and reaction-diffusion equations,, Ann. Probab., 13 (1985), 639.
|
[14] |
D. Hilhorst, R. Kersner, E. Logak and M. Mimura, Interface dynamics of the Fisher equation with degenerate diffusion,, J. Differential Equations, 244 (2008), 2872.
|
[15] |
A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Etude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique,, Bulletin Universit\'e d'Etat Moscou, (1937), 1. Google Scholar |
[16] |
H. Malchow, S. V. Petrovskii and E. Venturino, "Spatiotemporal Patterns in Ecology and Epidemiology. Theory, Models, and Simulations,", Mathematical and Computational Biology Series, (2008).
|
[17] |
S. V. Petrovskii and H. Malchow, eds. (2005), "Biological Invasions in a Mathematical Perspective,", (A special issue of Biological Invasions: Proceedings of Computational and Mathematical Population Dynamics, (2004), 21. Google Scholar |
[18] |
N. Shigesada and K. Kawasaki, "Biological Invasion: Theory and Practise,", Oxford University Press, (1997). Google Scholar |
[19] |
S. Vakulenko and V. Volpert, Generalized travelling waves for perturbed monotone reaction-diffusion systems,, Nonlinear Anal., 46 (2001), 757.
|
[20] |
A. Volpert, V. Volpert, V. Volpert, "Travelling Wave Solutions of Parabolic Systems,", Translations of Mathematical Monographs, (1994).
|
[1] |
Patrick Martinez, Judith Vancostenoble. Lipschitz stability for the growth rate coefficients in a nonlinear Fisher-KPP equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 695-721. doi: 10.3934/dcdss.2020362 |
[2] |
Zhenzhen Wang, Tianshou Zhou. Asymptotic behaviors and stochastic traveling waves in stochastic Fisher-KPP equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020323 |
[3] |
Feifei Cheng, Ji Li. Geometric singular perturbation analysis of Degasperis-Procesi equation with distributed delay. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 967-985. doi: 10.3934/dcds.2020305 |
[4] |
Michiel Bertsch, Danielle Hilhorst, Hirofumi Izuhara, Masayasu Mimura, Tohru Wakasa. A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3117-3142. doi: 10.3934/dcds.2019226 |
[5] |
Helmut Abels, Johannes Kampmann. Existence of weak solutions for a sharp interface model for phase separation on biological membranes. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 331-351. doi: 10.3934/dcdss.2020325 |
[6] |
Eduard Marušić-Paloka, Igor Pažanin. Homogenization and singular perturbation in porous media. Communications on Pure & Applied Analysis, 2021, 20 (2) : 533-545. doi: 10.3934/cpaa.2020279 |
[7] |
Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020345 |
[8] |
Nicolas Rougerie. On two properties of the Fisher information. Kinetic & Related Models, 2021, 14 (1) : 77-88. doi: 10.3934/krm.2020049 |
[9] |
Manxue You, Shengjie Li. Perturbation of Image and conjugate duality for vector optimization. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020176 |
[10] |
Hua Zhong, Xiaolin Fan, Shuyu Sun. The effect of surface pattern property on the advancing motion of three-dimensional droplets. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020366 |
[11] |
Soonki Hong, Seonhee Lim. Martin boundary of brownian motion on Gromov hyperbolic metric graphs. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021014 |
[12] |
Craig Cowan, Abdolrahman Razani. Singular solutions of a Lane-Emden system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 621-656. doi: 10.3934/dcds.2020291 |
[13] |
Xinfu Chen, Huiqiang Jiang, Guoqing Liu. Boundary spike of the singular limit of an energy minimizing problem. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3253-3290. doi: 10.3934/dcds.2020124 |
[14] |
Shin-Ichiro Ei, Hiroshi Ishii. The motion of weakly interacting localized patterns for reaction-diffusion systems with nonlocal effect. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 173-190. doi: 10.3934/dcdsb.2020329 |
[15] |
Peter Frolkovič, Viera Kleinová. A new numerical method for level set motion in normal direction used in optical flow estimation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 851-863. doi: 10.3934/dcdss.2020347 |
[16] |
Shiqiu Fu, Kanishka Perera. On a class of semipositone problems with singular Trudinger-Moser nonlinearities. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020452 |
[17] |
Franck Davhys Reval Langa, Morgan Pierre. A doubly splitting scheme for the Caginalp system with singular potentials and dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 653-676. doi: 10.3934/dcdss.2020353 |
[18] |
Susmita Sadhu. Complex oscillatory patterns near singular Hopf bifurcation in a two-timescale ecosystem. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020342 |
[19] |
Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020442 |
[20] |
Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020 |
2019 Impact Factor: 1.105
Tools
Metrics
Other articles
by authors
[Back to Top]