Geodesic
Solution blow-up for a new stationary Sobolev-type equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 5, pp. 876-893 
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/
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     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},
     year = {2010},
     volume = {50},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a7/}
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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 $\eta<0$, 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.

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