Geodesic
Some questions in the theory of nonlinear elliptic and parabolic equations
Sbornik. Mathematics, Tome 23 (1974) no. 2, pp. 287-318 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the nonlinear parabolic equation of order $m$ \begin{equation} \frac{\partial u}{\partial t}=-A(D)u+f(u,D^\gamma u),\qquad|\gamma|\leqslant m, \end{equation} where the nonlinear part $f$ depends analytically on its arguments, in the case of periodic boundary conditions we prove a theorem about the unique solvability in a certain space of generalized functions if the initial condition is a eneralized function from the same class. We prove an analogous theorem for nonlinear elliptic equations. We construct an asymptotic expansion (as $t\to\infty$) for the $\xi$th Fourier coefficient $v(t,\xi)$ of the solution $u(t,x)$ of a parabolic equation of the form (1). Bibliography: 3 titles. 
@article{SM_1974_23_2_a7,
     author = {M. I. Vishik and A. V. Fursikov},
     title = {Some questions in the theory of nonlinear elliptic and parabolic equations},
     journal = {Sbornik. Mathematics},
     pages = {287--318},
     year = {1974},
     volume = {23},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_23_2_a7/}
}
TY  - JOUR
AU  - M. I. Vishik
AU  - A. V. Fursikov
TI  - Some questions in the theory of nonlinear elliptic and parabolic equations
JO  - Sbornik. Mathematics
PY  - 1974
SP  - 287
EP  - 318
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1974_23_2_a7/
LA  - en
ID  - SM_1974_23_2_a7
ER  - 
%0 Journal Article
%A M. I. Vishik
%A A. V. Fursikov
%T Some questions in the theory of nonlinear elliptic and parabolic equations
%J Sbornik. Mathematics
%D 1974
%P 287-318
%V 23
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1974_23_2_a7/
%G en
%F SM_1974_23_2_a7
M. I. Vishik; A. V. Fursikov. Some questions in the theory of nonlinear elliptic and parabolic equations. Sbornik. Mathematics, Tome 23 (1974) no. 2, pp. 287-318. http://geodesic.mathdoc.fr/item/SM_1974_23_2_a7/

[1] M. Rosenblatt, “Remarks on the Burgers equation”, J. of math. physics, 9:7 (1968), 1129–1136 | DOI | MR | Zbl

[2] M. I. Vishik, A. V. Fursikov, “Analiticheskie pervye integraly nelineinykh parabolicheskikh v smysle I. G. Petrovskogo sistem differentsialnykh uravnenii i ikh prilozheniya”, Uspekhi matem. nauk, XXIX:2 (176) (1974), 123–153

[3] M. I. Vishik, A. V. Fursikov, “Analiticheskie pervye integraly nelineinykh parabolicheskikh uravnenii i ikh prilozheniya”, Matem. sb., 92(134) (1973), 347–377 | MR