Existence and non-existence of global solutions for nonlinear hyperbolic equations of higher order
Chen, Guo Wang ; Wang, Shu Bin
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 475-487 / Harvested from Czech Digital Mathematics Library
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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 $$ u_{tt}-\left[ a_0+n a_1(u_x)^{n-1}\right]u_{xx}-a_2 u_{xxtt}=0. $$

Publié le : 1995-01-01
Classification:  35L35,  35L75,  35Q72,  74H45,  74K10 
@article{118776,
     author = {Guo Wang Chen and Shu Bin Wang},
     title = {Existence and non-existence of global solutions for nonlinear hyperbolic equations  of higher order},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {475-487},
     zbl = {0839.35085},
     mrnumber = {1364488},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118776}
}

Chen, Guo Wang; Wang, Shu Bin. Existence and non-existence of global solutions for nonlinear hyperbolic equations  of higher order. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 475-487. http://gdmltest.u-ga.fr/item/118776/

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