Travelling fronts for multidimensional nonlinear transport equations
Schwetlick, Hartmut R.
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000), p. 523-550 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2000-01-01
@article{AIHPC_2000__17_4_523_0,
     author = {Schwetlick, Hartmut R.},
     title = {Travelling fronts for multidimensional nonlinear transport equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {17},
     year = {2000},
     pages = {523-550},
     mrnumber = {1782743},
     zbl = {0965.45012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2000__17_4_523_0}
}

Schwetlick, Hartmut R. Travelling fronts for multidimensional nonlinear transport equations. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) pp. 523-550. http://gdmltest.u-ga.fr/item/AIHPC_2000__17_4_523_0/

[1] Aronson D.G., The asymptotic speed of propagation of a simple epidemic, in: Fitzgibbon W.E., Walker H.F. (Eds.), Nonlinear Diffusion, Res. Notes Math., Vol. 14, Pitman, 1977, pp. 1-23. | MR 490046 | Zbl 0361.35011

[2] Aronson D.G., Weinberger H.F., Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in: Goldstein J. (Ed.), Partial Differential Equations and Related Topics, Lect. Notes Math., Vol. 446, Springer, 1975, pp. 5- 49. | MR 427837 | Zbl 0325.35050

[3] Aronson D.G., Weinberger H.F., Multidimensional nonlinear diffusion arising in population genetics, Adv. Math. 30 (1978) 33-76. | MR 511740 | Zbl 0407.92014

[4] Berestycki H., Larrouturou B., A semilinear elliptic equation in a strip arising in a two-dimensional flame propagation model, J. Reine Angew. Math. 396 (1989) 14-40. | MR 988546 | Zbl 0658.35036

[5] Berestycki H., Nirenberg L., Travelling fronts in cylinders, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 9 (5) (1992) 497-572. | Numdam | MR 1191008 | Zbl 0799.35073

[6] Diekmann O., Run for your life. A note on the asymptotic speed of propagation of an epidemic, J. Differential Equations 33 (1979) 58-73. | MR 540817 | Zbl 0377.45007

[7] Fisher R.A., The advance of advantageous genes, Ann. Eugenics 7 (1937) 355-369. | JFM 63.1111.04

[8] Golse F., Lions P.-L., Perthame B., Sentis R., Regularity of the moments of the solution of a transport equation, J. Functional Analysis 79 (1) (1988) 110-125. | MR 923047 | Zbl 0652.47031

[9] Hadeler K.P., Travelling fronts for correlated random walks, Can. Appl. Math. Q. 2 (1) (1994) 27-43. | MR 1271437 | Zbl 0802.60065

[10] Hadeler K.P., Reaction transport systems in biological modelling, in: Mathematics Inspired by Biology, Lect. Notes Math., Vol. 1714, Springer, 1999. | MR 1737306 | Zbl 1002.92506

[11] Kolmogorov A.N., Petrovsky I.G., Piscounov N.S., Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bull. Univ. État Moscou, Ser. Int., Sect. A, Math. et Mecan. 1 (6) (1937) 1-25; English Transl. in: Pelcé R. (Ed.), Dynamics of Curved Fronts, Academic Press, 1988, p. 105-130. | Zbl 0018.32106

[12] Othmer H.G., Dunbar S.R., Alt W., Models of dispersal in biological systems, J. Math. Biol. 26 (3) (1988) 263-298. | MR 949094 | Zbl 0713.92018

[13] Schumacher K., Travelling-front solutions for integro-differential equations. I, J. Reine Angew. Math. 316 (1980) 54-70. | MR 581323 | Zbl 0419.45004

[14] Thieme H.R., Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations, J. Reine Angew. Math. 306 (1979) 94-121. | MR 524650 | Zbl 0395.45010

[15] Weinberger H.F., Asymptotic behavior of a model in population genetics, in: Chadam J.M. (Ed.), Nonlinear Partial Differential Equations and Applications, Lect. Notes Math., Vol. 648, Springer, 1978, pp. 47-96. | MR 490066 | Zbl 0383.35034

[16] Weinberger H.F., Long-time behavior of a class of biological models, SIAM J. Math. Anal. 13 (3) (1982) 353-396. | MR 653463 | Zbl 0529.92010