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Existence and uniqueness of global solutions to a class of Boussinesq type equations. (Chinese) Zbl 1249.35057
Summary: In this paper, the existence and uniqueness of global generalized solutions and global classical solutions to the Cauchy problem for a class of Boussinesq type equations of sixth order are proved. Some sufficient conditions of blow up of solutions to this Cauchy problem in finite time are also given.
MSC:
35G25Initial value problems for nonlinear higher-order PDE
35L30Higher order hyperbolic equations, initial value problems