Geodesic
Methods of constructing approximate self-similar solutions of nonlinear heat equations. III
Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 1-18 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A rather general approach to the investigation of the asymptotic behavior of solutions of quasilinear parabolic heat equations $$ \frac{\partial u}{\partial t}=\frac\partial{\partial x}\biggl(k(u)\frac{\partial u}{\partial x}\biggr);\qquad k(u)>0,\quad u>0. $$ is proposed. The investigation is carried out by constructing so-called approximate self-similar solutions (ap.s-s.s's.) which do not satisfy the equation but to which solutions of the problems considered converge asymptotically. A system of ap.s-s.s's. which is complete in a particular sense is constructed for the case where the coefficient $k(u)$ satisfies the condition $[k(u)/k'(u)]'\to0$ as $u\to+\infty$ (for example, $k(u)=\exp(u^\lambda)$, $\lambda>0$; $k(u)=\exp(\exp u)$, etc.). Bibliography: 4 titles. 
@article{SM_1984_48_1_a0,
     author = {V. A. Galaktionov and A. A. Samarskii},
     title = {Methods of constructing approximate self-similar solutions of nonlinear heat {equations.~III}},
     journal = {Sbornik. Mathematics},
     pages = {1--18},
     year = {1984},
     volume = {48},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_48_1_a0/}
}
TY  - JOUR
AU  - V. A. Galaktionov
AU  - A. A. Samarskii
TI  - Methods of constructing approximate self-similar solutions of nonlinear heat equations. III
JO  - Sbornik. Mathematics
PY  - 1984
SP  - 1
EP  - 18
VL  - 48
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1984_48_1_a0/
LA  - en
ID  - SM_1984_48_1_a0
ER  - 
%0 Journal Article
%A V. A. Galaktionov
%A A. A. Samarskii
%T Methods of constructing approximate self-similar solutions of nonlinear heat equations. III
%J Sbornik. Mathematics
%D 1984
%P 1-18
%V 48
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1984_48_1_a0/
%G en
%F SM_1984_48_1_a0
V. A. Galaktionov; A. A. Samarskii. Methods of constructing approximate self-similar solutions of nonlinear heat equations. III. Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 1-18. http://geodesic.mathdoc.fr/item/SM_1984_48_1_a0/

[1] Galaktionov V. A., Samarskii A. A., “Metody postroeniya priblizhennykh avtomodelnykh reshenii nelineinykh uravnenii teploprovodnosti. I”, Matem. sb., 118 (160) (1982), 291–322 | MR | Zbl

[2] Galaktionov V. A., Samarskii A. A., “Metody postroeniya priblizhennykh avtomodelnykh reshenii nelineinykh uravnenii teploprovodnosti. II”, Matem. sb., 118 (160) (1982), 435–455 | MR | Zbl

[3] Ovsyannikov L. V., “Gruppovye svoistva uravneniya nelineinoi teploprovodnosti”, DAN SSSR, 125:3 (1959), 492–495 | Zbl

[4] Atkinson F. V., Peletier L. A., “Similarity solutions of the nonlinear diffusion equation”, Arch. for Ration. Mech. and Anal., 54 (1974), 373–392 | DOI | MR | Zbl