[PDF] Top 20 Blow up of Solutions for a System of Nonlinear Higher order Kirchhoff type Equations

... 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 ... See full document

... the equations, they established several results concerning local existence, glo- bal existence, uniqueness, and finite time blow-up (the initial energy E(0) < 0) ...latter blow-up ... See full document

... for blow-up ...for blow-up time of a system of ...for blow-up time of the solutions to two nonlinear wave ... See full document

... the system toward stability, while the nonlinear source term f (u) models an external force that amplifies the energy and drives the system to possible solutions that blow up in ... See full document

... [17] Ling Chen, Wei Wang, Guoguang Lin. The global attractor and their Hausdorff and Fractal dimensions estimation for the higher-order nonlinear Kirchhoff-type equation [J]. ... 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

... for nonlinear Kirchhoff type equations with higher-order strong damping is considered by using the Hadamard graph transformation ...in order to acquire the result of the ... See full document

... This paper is organized as follows: In Section 2, we recall many basic concepts related to a random attractor for genneral random dynamical system. In Section 3, we introduce O-U process and deal with random term. ... See full document

... of solutions of sto- chastic higher-order Kirchhoff equation with strong damping of white noise, nonlinear and non-local source terms and the existence of attractors of stochas- tic ... See full document

... (the nonlinear alternative of Leray-Schauder) Let X be a normed linear space, S ⊂ X be a convex set, U be open in S with 0 ∈ U, and F : U → S be a continuous and compact ... See full document

... coupled Kirchhoff-type ...the system. For this problem, we will study the exponential attractors, blow-up, random attractors and so ... See full document

... and blow-up of solutions for nonlinear wave equations of higher-order Kirchhoff type with strong ...nondenerate Kirchhoff equation, and derive the ... See full document

... G. G. Lin and L. J., Hu have studied the existence of a global attractor for coupled Kirchhoff type equations with strongly linear damping in [1]. In this paper, we are concerned with the finite ... See full document

... Ikehata, On global solutions and energy decay for the wave equations of the Kirchhoff type with nonlinear damping terms, J.. Messaoudi, Blow up in a nonlinearly damped wave equation, Mat[r] ... See full document

... ∂ − ∂ ∆ − ∆ + = ∇ ⋅ ∇ + (1.6) In bounded 3D domains. This method establishes the existence and uniqueness of energy solutions in the case where the growth exponent of the non-linearity φ is less than 6 and f may ... See full document

... The paper is organized as follows. In Section , we introduce some notations and the variational framework for (.), and then establish compactness conditions. In Section , we prove Theorem . and Theorem .. In the ... See full document

... tion between the linear damping (q = ) and source term by using a concavity method. But this method cannot be applied in the case of a nonlinear damping term. Georgiev and Todorova [] extended Levine’s result to ... See full document

... Georgiev, “Blow up of the solutions of nonlinear wave equation in Reissner-Nordstr¨om metric,” Dynamics of Partial Di ff erential Equations , vol.[r] ... See full document

... 2 The existence of uncountably many bounded nonoscillatory solutions Now we investigate sufficient conditions for the existence of uncountably many bounded nonoscillatory solutions of (.) under various ... See full document

... where a, l > 0 and Ω is a bounded domain in R N (N ≥ 1) with smooth boundary ∂Ω . There have been many articles dealing with properties of solutions to degenerate parabolic equations with homogeneous ... See full document