Solution blow-up for a new stationary Sobolev-type equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 5, pp. 876-893
Voir la notice de l'article provenant de la source Math-Net.Ru
A new nonlinear stationary Sobolev-type equation with a parameter $\eta\in\mathbb{R}^1$ is derived. For $\eta>0$, global solvability in the weak generalized sense is proved in the entire waveguide $\mathbb{S}\otimes\mathbb{R}_+^1$. For $\eta0$, the strong generalized solution is shown to blow up in a certain waveguide cross section $z=R_0>0$. An upper bound for $R_0$ in terms of the original parameters of the problem is obtained.
@article{ZVMMF_2010_50_5_a7,
author = {M. O. Korpusov and A. G. Sveshnikov},
title = {Solution blow-up for a new stationary {Sobolev-type} equation},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {876--893},
publisher = {mathdoc},
volume = {50},
number = {5},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a7/}
}
TY - JOUR AU - M. O. Korpusov AU - A. G. Sveshnikov TI - Solution blow-up for a new stationary Sobolev-type equation JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2010 SP - 876 EP - 893 VL - 50 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a7/ LA - ru ID - ZVMMF_2010_50_5_a7 ER -
%0 Journal Article %A M. O. Korpusov %A A. G. Sveshnikov %T Solution blow-up for a new stationary Sobolev-type equation %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2010 %P 876-893 %V 50 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a7/ %G ru %F ZVMMF_2010_50_5_a7
M. O. Korpusov; A. G. Sveshnikov. Solution blow-up for a new stationary Sobolev-type equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 5, pp. 876-893. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a7/