zbMATH — the first resource for mathematics

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

35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35A35 Theoretical approximation in context of PDEs
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.