Multidimensional nonlinear diffusion arising in population genetics

Advances in Mathematics - Tập 30 Số 1 - Trang 33-76 - 1978
D. G. Aronson1, Hans F. Weinberger1
1School of Mathematics, University of Minnesota 127 Vincent Hall, Minneapolis, Minnesota 55455, USA.

Tóm tắt

Từ khóa


Tài liệu tham khảo

Aronson, 1975, Nonlinear diffusion in population genetics, combustion, and nerve propagation, Vol. 446, 5

Chafee, 1974, A stability analysis for a semilinear parabolic partial differential equation, J. Differential Eqs., 15, 522, 10.1016/0022-0396(74)90071-0

Fisher, 1937, The advance of advantageous genes, Ann. of Eugenics, 7, 355, 10.1111/j.1469-1809.1937.tb02153.x

Friedman, 1964

Fujita, 1966, On the blowing up of solutions of the Cauchy problem for ut = Δu + u1 + α, J. Fac. Sci. Univ. Tokyo, (I), 13, 109

Gelfand, 1959, Some problems in the theory of quasilinear equations, Uspehi Math. Nauk, 14, 87

1963, Amer. Math. Soc. Trans., 29, 295, 10.1090/trans2/029/12

Hayakawa, 1973, On nonexistence of global solutions of some semilinear parabolic equations, 49, 503

Kanel', 1961, The behavior of solutions of the Cauchy problem when time tends to infinity, in the case of quasilinear equations arising in the theory of combustion, Dokl. Akad. Nauk S.S.S.R., 132, 268

1960, Soviet Math. Dokl., 1, 533

Kanel', 1961, Certain problems on equations in the theory of burning, Dokl. Akad. Nauk S.S.S.R., 136, 277

1961, Soviet Math. Dokl., 2, 48

Kanel', 1962, Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory, Mat. Sbornik, 59, 245

Kanel', 1964, On the stability of solutions of the equations of combustion theory for finite initial functions, Mat. Sbornik, 65, 398

Kobayashi, 1977, On the growing up problem for semilinear heat equations, J. Math. Soc. Japan, 29, 407, 10.2969/jmsj/02930407

Kolmogoroff, 1937, Étude de l'équations de la diffusion avec croissance de la quantité de matière et son application a un problème biologique, Bull. Univ. Moscow, Ser. Internat., Sec. A, 1, 1

Petrovski, 1966

Petrovski, 1973

Protter, 1967

T. Sirao, On the growing up problem for semilinear heat equations, Kokyuroku of the Inst. of Math., Anal., Kyoto Univ., in press.