Geodesic
On a class of nonlocal parabolic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1056-1063

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a boundary value problem for parabolic equations with nonlocal nonlinearity of such a form that favorably differs from other equations in that it leads to partial differential equations that have important properties of ordinary differential equations. Local solvability and uniqueness theorems are proved, and an analog of the Painlevé singular nonfixed points theorem is proved. In this case, there is an alternative – either a solution exists for all $t\ge0$ or it goes to infinity in a finite time $t=T$ (blowup mode). Sufficient conditions for the existence of a blowup mode are given. 
@article{ZVMMF_2011_51_6_a7,
     author = {A. N. Bogolyubov and M. D. Malykh},
     title = {On a~class of nonlocal parabolic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1056--1063},
     publisher = {mathdoc},
     volume = {51},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a7/}
}
TY  - JOUR
AU  - A. N. Bogolyubov
AU  - M. D. Malykh
TI  - On a class of nonlocal parabolic equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1056
EP  - 1063
VL  - 51
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a7/
LA  - ru
ID  - ZVMMF_2011_51_6_a7
ER  - 
%0 Journal Article
%A A. N. Bogolyubov
%A M. D. Malykh
%T On a class of nonlocal parabolic equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1056-1063
%V 51
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a7/
%G ru
%F ZVMMF_2011_51_6_a7
A. N. Bogolyubov; M. D. Malykh. On a class of nonlocal parabolic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1056-1063. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a7/