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Existence and non-existence of global solutions for a class of nonlinear wave equations. (English) Zbl 1007.35046

The paper deals with the nonlinear wave equation of fourth order \(u_{tt}+u_{xxxx}=\sigma(u_{x})_{x}+f(x,t)\) and the Boussinesq-type equation \(u_{tt}+u_{xxxx}=\sigma(u)_{xx}+f(x,t)\) \((x\in (0,1), t>0).\) Existence of global generalized and classical solutions as well as blow-up of solutions to initial-boundary value problems for these equations are established.

MSC:

35L35 Initial-boundary value problems for higher-order hyperbolic equations
35L75 Higher-order nonlinear hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
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