Displaying similar documents to “Local energy decay for waves governed by a system of nonlinear Schrödinger equations in a nonuniform medium.”

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.

Stability of vibrations for some Kirchhoff equation with dissipation

Prasanta Kumar Nandi, Ganesh Chandra Gorain, Samarjit Kar (2014)

Applications of Mathematics

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In this paper we consider the boundary value problem of some nonlinear Kirchhoff-type equation with dissipation. We also estimate the total energy of the system over any time interval [ 0 , T ] with a tolerance level γ . The amplitude of such vibrations is bounded subject to some restrictions on the uncertain disturbing force f . After constructing suitable Lyapunov functional, uniform decay of solutions is established by means of an exponential energy decay estimate when the uncertain disturbances...