On the nonexistence of global solutions of some initial-boundary value problems for the Korteweg-de Vries equation

摘要

We consider the problem of finite-time blow-up of solutions of a class of initial-boundary value problems for the Korteweg-de Vries equation. By using the method of optimal test functions corresponding to the boundary conditions, we obtain blow-up conditions for local (with respect to t > 0) solutions and estimate the blow-up time.