Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation |
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Authors: | Qingyong Gao Fushan Li Yanguo Wang |
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Affiliation: | 1.School of Mathematical Sciences,Qufu Normal University,Qufu,PR China |
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Abstract: | In this paper, we consider the nonlinear Kirchhoff-type equation $
u_{tt} + M(left| {D^m u(t)} right|_2^2 )( - Delta )^m u + left| {u_t } right|^{q - 2} u_t = left| {u_t } right|^{p - 2} u
$
u_{tt} + M(left| {D^m u(t)} right|_2^2 )( - Delta )^m u + left| {u_t } right|^{q - 2} u_t = left| {u_t } right|^{p - 2} u
with initial conditions and homogeneous boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time. |
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