Geodesic
Front motion in a parabolic reaction-diffusion problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 276-285 Cet article a éte moissonné depuis la source Math-Net.Ru

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A singularly perturbed initial-boundary value problem is considered for a parabolic equation known in applications as the reaction-diffusion equation. An asymptotic expansion of solutions with a moving front is constructed, and an existence theorem for such solutions is proved. The asymptotic expansion is substantiated using the asymptotic method of differential inequalities, which is extended to the class of problems under study. The method is based on well-known comparison theorems and is a development of the idea of using formal asymptotics for the construction of upper and lower solutions in singularly perturbed problems with internal and boundary layers. 
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Yu. V. Bozhevol'nov; N. N. Nefëdov. Front motion in a parabolic reaction-diffusion problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 276-285. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a7/

[1] Vasileva A. B., Butuzov V. F., Nefedov N. N., “Kontrastnye struktury v singulyarno vozmuschennykh zadachakh”, Fund. i prikl. matem., 1998, no. 4, 899–851 | MR

[2] Butuzov V. F., Nefedov N. N., Shnaider K. R., “O formirovanii i rasprostranenii rezkikh perekhodnykh sloev v parabolicheskikh zadachakh”, Vestn. MGU. Ser. 3. Fiz., astron., 2005, no. 1, 9–13 | MR | Zbl

[3] Fife P. C., Hsiao L., “The generation and propagation of internal layers”, Nonlinear Analys. Theory Methods Appl., 12:1 (1998), 19–41 | DOI | MR

[4] Volkov V. T., Grachev N. E., Nefedov N. N., Nikolaev A. N., “O formirovanii rezkikh perekhodnykh sloev v dvumernykh modelyakh reaktsiya–diffuziya”, Zh. vychisl. matem. i matem. fiz., 47:8 (2007), 1356–1364 | MR

[5] Nefedov N. N., Radziunas M., Schneider K. R., Vasil'eva A. B., “Change of the type of contrast structures in parabolic Neumann-problems”, Zh. vychisl. matem. i matem. fiz., 45:1 (2005), 41–55 | MR | Zbl

[6] Nefedov N. N., “Metod differentsialnykh neravenstv dlya nekotorykh klassov nelineinykh singulyarno vozmuschennykh zadach s vnutrennimi sloyami”, Differents. ur-niya, 31:7 (1995), 1142–1149 | MR | Zbl

[7] Vasileva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vyssh. shkola, M., 1990 | MR

[8] Pao C. V., Nonlinear parabolic and elliptic equations, Plenum Press, New York, 1992 | MR

[9] Amann H., “Periodic solutions of semilinear parabolic equations”, Nonlinear Analysis, Collection of Papers in Honor of Erich Rothe, Acad., New York, 1978, 1–29 | MR

[10] Sattinger D. H., “Monotone methods in elliptic and parabolic boundary value problems”, Indiana Univ. Math. J., 21:11 (1972), 979–1001 | DOI | MR

[11] Fife P. C., Tang M., “Comparision principles for reaction-diffusion systems: Irregular comparision functions and applications to question of stability and speed propagation of disturbances”, J. Different. Equations, 40 (1981), 168–185 | DOI | MR | Zbl