Abstract
This paper studies the absence of the global solutions to the fifth-order KdV equations in the form, ∂ t u + ∂ x 5 u = b 1 u ∂ x u + c 1 ∂ x u ∂ x 2 u + c 2 u ∂ x 3 u , x ∈ R , t ∈ R + . As the initial data u ( 0 , x ) ∈ L 1 ( R ) , the coefficients b 1 > − c 1 and c 1 = c 2 < 0 , we use the method of nonlinear capacity, developed by Galaktionov, Pokhozhaev and Mitidieri, and obtain several sufficient conditions of nonexistence of global solutions.
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