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- W113582954 abstract "The purpose of this paper is to give a precise description of the asymptotic behavior for solutions which blow-up in finite positive time T. This multiple existence of solutions complicates the stability analysis required to precisely describe the evolution of the time-dependent solutions u(z,t) near the blow-up singularity. The results of Giga-Kohn and Bebernes-Bressan-Eberly to the dimensions ngreater than or equal to3 are extended by proving that, in spite of the multiple existence of solutions the asymptotic formulas remain the same as in dimensions 1 and 2. The key to unraveling these problems is a precise understanding of the behavior of the nonconstant solution relative to a singular solution given in equation form. The real difficulty in understanding how the single point blow-up occurs rests on determining the nonincreasing globally Lipschitz continuous solutions of an associated steady-state equation." @default.
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- W113582954 date "1986-01-01" @default.
- W113582954 modified "2023-09-23" @default.
- W113582954 title "A description of self-similar blow-up for dimensions ngreater than or equal to3" @default.
- W113582954 hasPublicationYear "1986" @default.
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