Displaying similar documents to “Exponential decay of energy for some nonlinear hyperbolic equations with strong dissipation.”

Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation

Qingyong Gao, Fushan Li, Yanguo Wang (2011)

Open Mathematics

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In this paper, we consider the nonlinear Kirchhoff-type equation u t t + M ( D m u ( t ) 2 2 ) ( - Δ ) m u + u t q - 2 u t = u t 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.