[PDF] Top 20 Long-Time Behavior of Solutions for a Class of Nonlinear Higher Order Kirchhoff Equation

... lower-order Kirchhoff-type equation studied by previous scholars, this paper studies the global attractor family and its finite dimension estimation for the higher-order ... See full document

... the long-time behavior of solu- tions of evolutionary equations, these inertial manifolds are smooth finite di- mensional invariant Lipschitz manifolds which contain the global attractor and attract ... See full document

... global solutions and blow up of solutions for the initial boundary value problem and Cauchy problem of ...the long-time behavior of ... See full document

... the behavior of solutions of a given differential equation and does not seek explicit ...of solutions to different equations, functional differential equations, and dynamical equation have ... See full document

... of time scales, which has recently received a lot of attention, was introduced by Hilger’s landmark paper 1 in order to create a theory that can unify continuous and discrete ...a time scale is equal ... See full document

... of Kirchhoff- type equations have been investigated by many authors, see, ...wave equation with multiplicative noise defined on unbounded domains, and investigate the existence of a random attractor, they ... See full document

... The content of this paper is organized as follows. In Section 2, we give some lemmas. In Section 3, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. In Section 4, ... See full document

... asymptotic behavior of solutions for higher-order Kirchhoff ...high-order Kirchhoff equation is very meaningful. In order to study the high-order ... See full document

... u x = u x u x = u x (8) where u u x t = ( ) , is the real function on U × [ 0, +∞ ) , α > 0 is the strong damping coefficient, β > 0 is the damping coefficient, and K > 0 is the dis- sipation coefficient. In ... See full document

... a nonlinear damping ...the nonlinear case (p > 1). They showed that solutions with negative initial energy blow up in finite ...the nonlinear damping and the solution has positive initial ... See full document

... energy solutions in the case where the growth exponent of the non-linearity φ is less than 6 and f may have arbitrary polynomial growth ...that equation and their additional regularity are also ...wave ... See full document

... a class of fourth-order wave equations in an n-dimensional ...of solutions to the corresponding linear equation, a solution space is ... See full document

... the equation. For more research on the global solutions and global attractors of Kirchhoff and sine-Gordon equations, we refer the reader to ... See full document

... with p =  and q = p +  = , for which it was shown that, for sufficiently large domains, the solutions of (.) must blow up in finite time regardless of the size of the initial value. The more general ... See full document

... In this paper, we consider the rule of trajectory structure for a kind of second-order rational difference equation. With the change of the initial values, we find the successive lengths of positive and ... See full document

... The most important characteristic of equation (.) or (.) is in that, generally, the uniqueness of the solutions is not true; one can refer to [–]. Thus, for the equation of the type (.), we ... See full document

... In this paper, we mainly deal with a class of higher-order coupled Kir- chhoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. ... See full document

... asymptotic behavior of the renewal equation consists in a convergence to a stationary ...1 solutions [5, 6, 8, 11, 14, 15, ...measure solutions in ... See full document

... 1) Equation (14) has a solution of type (D) if and only if σ ≥ − − α 1 (Theorem ...2) Equation (14) has a solution of type (AC) if and only if σ < − − α 1 (Theorem ...3) Equation (14) has a ... See full document

... Motivated by the above work, by using the modified comparison argument, the self- similar transformation method, and the half-relaxed limits technique used in [, , ], we investigate the asymptotic behavior of ... See full document