The Inertial Manifolds for a Class of Higher-Order Coupled Kirchhoff-Type Equations

Blow up of Solutions for a System of Nonlinear Higher-order Kirchhoff-type Equations

In this work, we consider the initial boundary value problem for the Kirchhoff-type equations with damping and source terms  utt +M (∫ Ω ∣∣∣(−△)m2 u∣∣∣2 dx) (−△) u+ |ut| ut = f1 (u, v) , vtt +M (∫ Ω ∣∣∣(−△)m2 v∣∣∣2 dx) (−△) v + |vt| vt = f2 (u, v) in a bounded domain. We prove the blow up of the solution with positive initial energy by using the technique of [26] with a modification in th...

Inertial Manifolds for Reaction Diffusion Equations in Higher Space Dimensions

In this paper we show that the scalar reaction di1rusion equationu/ = v6.u + f(x, u),UERwith x E On C Rn (n = 2,3) and with Dirichlet, Neumann, or peri-odic boundary conditions, has an inertial manifold when (1) the equation isdissipative, and (2) f is of class C3 and for 03 = (O,2n:)3 or Oz =(O,2n:/at> x (0, 2n:/az), where al and az are positive. The proof is basedo...

the investigation of the relationship between type a and type b personalities and quality of translation

چکیده ندارد.

The variational iteration method for a class of tenth-order boundary value differential equations

Stochastic inertial manifolds for damped wave equations ∗

In this paper, stochastic inertial manifold for damped wave equations subjected to additive white noise is constructed by the Lyapunov-Perron method. It is proved that when the intensity of noise tends to zero the stochastic inertial manifold converges to its deterministic counterpart almost surely.