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

Guo Wang ChenShu 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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