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

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Chen Guowang, Wang Shubin

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

Comment.Math.Univ.Carolinae 36,3 (1995) 475-487.

Abstract: 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

utt−αuxx−βuxxtt=ϕ(ux)x

are proved. Finally, the results of the above problem are applied to the equation arising from nonlinear waves in elastic rods

utt−£

a0+na1(ux)n−1¤

uxx−a2uxxtt= 0.

Keywords: nonlinear hyperbolic equation, initial boundary value problem, classi- cal global solution, blow up of solutions

AMS Subject Classification: 35L35

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