Displaying similar documents to “On the strongly damped wave equation with nonlinear damping and source terms.”

Blow-up of solutions for a viscoelastic equation with nonlinear damping

Yang Zhifeng (2008)

Open Mathematics

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The initial boundary value problem for a viscoelastic equation with nonlinear damping in a bounded domain is considered. By modifying the method, which is put forward by Li, Tasi and Vitillaro, we sententiously proved that, under certain conditions, any solution blows up in finite time. The estimates of the life-span of solutions are also given. We generalize some earlier results concerning this equation.

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.