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A phase plane discussion of convergence to travelling fronts for nonlinear diffusion. (English) Zbl 0459.35044

MSC:
35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35A35 Theoretical approximation in context of PDEs
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[1] Chueh, K.-N., On the asymptotic behavior of solutions of semilinear parabolic partial differential equations. Ph. D. Thesis, University of Wisconsin, 1975.
[2] Fife, P. C., & J. B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions. Arch. Rational Mech. Anal., 65, 335–361 (1977). · Zbl 0361.35035 · doi:10.1007/BF00250432
[3] Friedman, A., Partial Differential Equations, New York: Holt, Rinehart and Winston 1969. · Zbl 0224.35002
[4] Kanel’, Ya. I., On the stabilization of solutions of the Cauchy problem for equations arising in the theory of combustion. Mat. Sbornik 59, 245–288 (1962). See also Dokl. Akad. Nauk SSSR 132, 268–271 (1960) (= Soviet Math. Dokl. 1, 533–536 (1960)), and Dokl. Akad. Nauk SSSR 136, 277–280 (1961) (= Soviet Math. Dokl. 2, 48–51 (1961)).
[5] Ladyzenskaja, O. A., Solonnikov, V. A., & N. N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type. Americal Mathematical Society Translations, Providence, R. I. (1968).
[6] Rothe, F., Convergence to travelling fronts in semilinear parabolic equations. Proc. Roy. Soc. Edinburgh, 80 A, 213–234 (1978). · Zbl 0389.35024 · doi:10.1017/S0308210500010258
[7] Uchiyama, K., The behavior of solutions of some nonlinear diffusion equations for large time. J. Math. Kyoto Univ., 18, 453–508 (1978). · Zbl 0408.35053 · doi:10.1215/kjm/1250522506
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