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 $$ u_{tt}-\alpha u_{xx}-\beta u_{xxtt}=\varphi (u_x)_x $$ are proved. Finally, the results of the above problem are applied to the equation arising from nonlinear waves in elastic rods $$ u_{tt}-\left [ a_0+n a_1(u_x)^{n-1}\right ]u_{xx}-a_2 u_{xxtt}=0. $$

Keywords: nonlinear hyperbolic equation, initial boundary value problem, classical global solution, blow up of solutions
AMS Subject Classification: 35L35

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