On the Boundary Behavior for the Blow-up Solutions of the sinh-Gordon Equation and Rank N Toda Systems in Bounded Domains
2018 ◽
Vol 2020
(23)
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pp. 9386-9419
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Keyword(s):
Blow Up
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Abstract In this paper we are concerned with the blow-up analysis of two classes of problems in bounded domains arising in mathematical physics: sinh-Gordon equation and some general rank $n$ Toda systems. The presence of a residual mass in the blowing up limit makes the analysis quite delicate; nevertheless, by exploiting suitable Pohozaev identities and a detailed blow-up analysis we exclude blowup at the boundary. This is the 1st result in this direction in the presence of a residual mass. As a byproduct we obtain general existence results in bounded domains.