Weighted identities for solutions of generalized Korteweg-de Vries equations
Consider the Korteweg-de Vries equation u t + u xxx + uu x = 0 and its generalization u t + u xxx + f(u)x = 0. For the solutions of these equations, weighted identities (differential and integral) are obtained. These identities make it possible to establish the blow-up (in finite time) of the solutions of certain boundary-value problems.
KeywordsKorteweg-de Vries equation initial boundary-value problem weighted differential inequality weighted integral inequality blow-up of solutions Hölder’s inequality Young’s inequality Dirichlet boundary condition
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