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Existence and non-existence of global solutions for nonlinear hyperbolic equations of higher order

Guo Wang Chen; Shu Bin Wang — 1995

Commentationes Mathematicae Universitatis Carolinae

The existence and uniqueness of classical global solution and blow up of non-global solution to the first boundary value problem and the second boundary value problem for the equation $u_{t t} - α u_{x x} - β u_{x x t t} = ϕ {(u_{x})}_{x}$ are proved. Finally, the results of the above problem are applied to the equation arising from nonlinear waves in elastic rods $u_{t t} - [a_{0} + n a_{1} {(u_{x})}^{n - 1}] u_{x x} - a_{2} u_{x x t t} = 0 .$

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