Solution blow-up for a new stationary Sobolev-type equation |
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Authors: | M O Korpusov A G Sveshnikov |
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Institution: | 1.Faculty of Physics,Moscow State University,Moscow,Russia |
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Abstract: | A new nonlinear stationary Sobolev-type equation with a parameter η ∈ ℝ1 is derived. For η > 0, global solvability in the weak generalized sense is proved in the entire waveguide $
\mathbb{S}
$
\mathbb{S}
⊗ ℝ+1. For η < 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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Keywords: | |
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