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Sixth International Conference on Differential and Functional Differential Equations DFDE-2011
August 17, 2011 10:00, Moscow
 


Blow-up solutions to the Korteweg–de Vries equation

S. I. Pohozaev

Steklov Mathematical Institute, Moscow, Russia
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S. I. Pohozaev


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Abstract: We deal with singular solutions to the Korteweg–de Vries equation which blow up at finite time. We examine solutions both for initial-boundary value problems and for the Cauchy problem.
We give an estimate of blow-up time depending on the boundary and initial conditions.
In conclusion, we demonstrate the explicit form of the blow-up solution of the Cauchy problem and show the mechanism of the blow-up of this solution.

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