Global Existence for Nonlinear Hyperbolic Systems of Kirchhoff Type

Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations ...

Global Existence and Decay Estimates for Nonlinear Kirchhoff–type Equation with Boundary Dissipation

In this paper, we consider the initial-boundary value problem for nonlinear Kirchhofftype equation utt −φ(‖∇u‖2)Δu−aΔut = b|u|β−2u, where a,b > 0 and β > 2 are constants, φ is a C1 -function such that φ(s) λ0 > 0 for all s 0 . Under suitable conditions on the initial data, we show the existence and uniqueness of global solution by means of the Galerkin method and the uniform decay rate of the e...

On a class of Kirchhoff type systems with nonlinear boundary condition

A class of Kirchhoff type systems with nonlinear boundary conditions considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

A blow-up result for a higher-order nonlinear Kirchhoff-type hyperbolic equation

In this work we consider a multi-dimensional higher-order Kirchhoff-type wave equation, with Dirichlet boundary conditions. We establish a blow-up result for certain solutions with positive initial energy. c © 2006 Elsevier Ltd. All rights reserved.

Existence and concentration of solutions for the nonlinear Kirchhoff type equations with steep well potential