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Kirchhoff-type Equation

Random Attractor of the Stochastic Strongly Damped for the Higher Order Nonlinear Kirchhoff Type Equation

Random Attractor of the Stochastic Strongly Damped for the Higher Order Nonlinear Kirchhoff Type Equation

... In this paper, we consider the stochastic higher-order Kirchhoff-type equation with nonlinear strongly dissipation and white noise. We first deal with ran- dom term by using Ornstein-Uhlenbeck ...

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The Global Attractors and Their Hausdorff and Fractal Dimensions Estimation for the Higher Order Nonlinear Kirchhoff Type Equation with Strong Linear Damping

The Global Attractors and Their Hausdorff and Fractal Dimensions Estimation for the Higher Order Nonlinear Kirchhoff Type Equation with Strong Linear Damping

... How to cite this paper: Gao, Y.L., Sun, Y.T. and Lin, G.G. (2016) The Global At- tractors and Their Hausdorff and Fractal Di- mensions Estimation for the Higher-Order Nonlinear Kirchhoff-Type ...

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The Global Attractors for the Higher Order Kirchhoff Type Equation with Nonlinear Strongly Damped Term

The Global Attractors for the Higher Order Kirchhoff Type Equation with Nonlinear Strongly Damped Term

... G. Kirchhoff [1] and has been studied by many authors under different types of ...of Kirchhoff equation, we can refer [2] [3] [4] [5] ...Higher-order Kirchhoff-type equation are ...

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General stability for the Kirchhoff-type equation with memory boundary and acoustic boundary conditions

General stability for the Kirchhoff-type equation with memory boundary and acoustic boundary conditions

... In this paper we consider the existence and general energy decay rate of global solution to the mixed problem for the Kirchhoff-type equation with memory boundary and acoustic boundary conditions. In order ...

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Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents

Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents

... 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] ...

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Global existence of solutions and energy decay for a Kirchhoff type equation with nonlinear dissipation

Global existence of solutions and energy decay for a Kirchhoff type equation with nonlinear dissipation

... 1 Introduction In this paper, we investigate the existence and asymptotic stability of global solutions for the initial boundary value problem of the following Kirchhoff-type equation wit[r] ...

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Multiplicity results for the Kirchhoff type equation via critical groups

Multiplicity results for the Kirchhoff type equation via critical groups

... Remark 1 Note that, for the semilinear elliptic equation, i.e., b = 0, Theorem 1.1 can be found in [2], now we can generalize the same results to Eq. (1.1) with any b > 0. However, we cannot directly use the ...

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Existence of Solutions for a Class of Kirchhoff type Equation with Nonstandard Growth

Existence of Solutions for a Class of Kirchhoff type Equation with Nonstandard Growth

... the Kirchhoff equations and the Kirchhoff systems have been considered by variational method in the case involving the p − Laplacian operator [4, 7, 8, 18, 19, ...

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Regularity of Global Attractors for the Kirchhoff Wave Equation

Regularity of Global Attractors for the Kirchhoff Wave Equation

... the Kirchhoff type equation with a strong dissipation and proved that the continuous semigroup S t ( ) possessed global attractors in the phase spaces with low ...the Kirchhoff wave ...

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On the Exponential Decay of Solutions for Some Kirchhoff Type Modelling Equations with Strong Dissipation

On the Exponential Decay of Solutions for Some Kirchhoff Type Modelling Equations with Strong Dissipation

... Let  be a bounded domain in R n with smooth boun- dary  . In this paper, we investigate the existence and the energy exponential decay estimate of global solutions for the initial boundary value problem of the ...

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Long-Time Behavior of Solutions for a Class of Nonlinear Higher Order Kirchhoff Equation

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 Kirchhoff-type ...

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

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

... Ono [16] considered equation (1.3) with M (s) = s γ , m = 1 and showed that the solution blow up if the initial energy is negative. Wu and Tsai [23] showed that the solution blow up under the condition of positive ...

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Global attractor for a nonlocal hyperbolic problem on ${\mathcal{R}}^{N}$

Global attractor for a nonlocal hyperbolic problem on ${\mathcal{R}}^{N}$

... In bounded domains there is a vast literature concerning the attractors of semilinear waves equa- tions. We refer to the monographs [2], [13]. Also in the paper [3] the existence of global attractor in a weak topology is ...

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4. Non-homogeneous Kirchhoff equation on $\mathbb{R}^3$

4. Non-homogeneous Kirchhoff equation on $\mathbb{R}^3$

... Remark. One can easily obtain that problem (1.1) admits two solutions which one has a positive energy and one has negative energy by using Ekeland’s variational principle and mountain pass theorem. As mentioned above, ...

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Energy decay for a viscoelastic Kirchhoff plate equation with a delay term

Energy decay for a viscoelastic Kirchhoff plate equation with a delay term

... where L is the length of the beam and α, β, γ are positive physical constants. Since then many mathematicians studied the related model in one dimension and higher dimensions. The main results are mainly concerned with ...

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A nonstandard higher-order variational model to speckle noise removal and thin-structure detection

A nonstandard higher-order variational model to speckle noise removal and thin-structure detection

... We can show the performance of our model for a more specific ultrasound medical images. From Figure 4, we can see that the p( · )-Kirchhoff model gives a good result compared with the TVL model, however the result ...

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Random Attractor Family for the Kirchhoff Equation of Higher Order with White Noise

Random Attractor Family for the Kirchhoff Equation of Higher Order with White Noise

... the equation into a stochastic KDV-type equation without white noise, the existence of stochastic attractors for dynamic systems deter- mined by the original equation is proved by discussing ...

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Global Attractors for a Class of Generalized Nonlinear Kirchhoff Sine Gordon Equation

Global Attractors for a Class of Generalized Nonlinear Kirchhoff Sine Gordon Equation

... u with respect to the variable t; u xx is the two-order partial derivative of the u about the independent variable x. Subsequently, Zhu [4] considered the following problem: u tt − α u t − u xx + λ g ( sin u ) = f x t ( ...

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Multiplicity of Nontrivial Solutions for Kirchhoff Type Problems

Multiplicity of Nontrivial Solutions for Kirchhoff Type Problems

... proposed by Kirchhoff 2 as an extension of the classical D’ Alembert’s wave equation for free vibrations of elastic strings. Kirchhoff’s model takes into account the changes in length of the string produced by ...

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The existence of positive solution for singular Kirchhoff equation with two parameters

The existence of positive solution for singular Kirchhoff equation with two parameters

... Since the method of sub-supersolutions is an important tool to solve the existence of so- lutions for boundary value problems, naturally, some authors hope to use the theorem of sub-supersolutions to discuss the elliptic ...

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