Existence of absorbing set for a nonlinear wave equation.

Kurt, Ayfer

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

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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.