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Initial value problem for a class of fourth-order nonlinear wave equations. (English) Zbl 1170.35473
Summary: Existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.
MSC:
35L30Higher order hyperbolic equations, initial value problems
35G25Initial value problems for nonlinear higher-order PDE
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