Damped Boussinesq Equation Research Articles

Conditional Regularity for the 3D Damped Boussinesq Equations with Zero Thermal Diffusion

Conditional Regularity for the 3D Damped Boussinesq Equations with Zero Thermal Diffusion

Superconvergence error analysis of Ciarlet-Raviart mixed finite element method for damped Boussinesq equation

The primary objective of this paper is to investigate the error analysis for the damped Boussinesq equation with the Ciarlet-Raviart mixed finite element method, focusing on achieving superconvergence. By employing a skillful mean technique and a high precision estimate of the bilinear element, as well as combining with projection and interpolation technique, we first obtain a superclose error estimate between interpolation of the exact solution and numerical solution. Subsequently, by applying an interpolation post-processing approach, we efficiently derive a global superconvergence result. Finally, several numerical results are presented to support our theoretical analysis.

Maximum Principle for the Damped Boussinesq equation

In this paper, the optimal distributed control problem of an Damped Boussinesq equation is studied. Dubovitskii-Milyutin functional analytical approach is formulated for obtaining the necessary optimality condition in the form of Maximum principle for the system under consideration. Necessary optimality condition is presented in fixed final horizon case.

Stratified Boussinesq equations with a velocity damping term

We consider an initial value problem of the multi-dimensional Boussinesq equations with velocity damping for strongly stratified fluids. We prove the global-in-time existence of the classical solution to the stratified damped Boussinesq equations with initial data near the stationary stratified solution . We also show the asymptotic stability of the solutions near the stratified solution and obtain the temporal decay for the fluid velocity and the temperature by providing estimates for the Green function associated with the linear operator in any dimension.

Analysis of Ciarlet–Raviart mixed finite element methods for solving damped Boussinesq equation

In this paper, we consider the numerical solution of damped Boussinesq equation using Ciarlet–Raviart mixed finite element method. An implicit finite difference scheme is used for the time discretization. A priori error estimates are analyzed and stability analysis of the method is shown. We obtain an optimal error estimate in L2 norm with quadratic or higher-order element, for both semi and fully discrete finite element approximations. Finally, numerical examples are given to verify the theoretical results.

Inviscid limit for the damped Boussinesq equation

In this paper, we consider the limit behavior of solutions to the Cauchy problem for damped Boussinesq equation in the regime of small viscosity in Rn. It is shown that the strong solutions of damped Boussinesq equation converge to a strong solution of Boussinesq equation in any time interval [0,T]. The key idea is that we only take into account the effect of dispersion and overlook the effect of dissipation in the damped Boussinesq equation, which is a kind of new view. We analyze the dispersion by the techniques of high-low frequency decomposition and Littlewood-Paley dyadic decomposition, stationary phase estimate and some properties of Bessel function.

A new global well-posedness for the damped Boussinesq equations

In this paper, we obtain global well-posedness for the d dimensional damped Boussinesq equations by assuming some new conditions. This means that the temperature may be large enough, provided that ϵ is a small enough constant.In this paper, we obtain global well-posedness for the d dimensional damped Boussinesq equations by assuming some new conditions. This means that the temperature may be large enough, provided that ϵ is a small enough constant.

On the Global Existence of Strong Solution to the 3D Damped Boussinesq Equations with Zero Thermal Diffusion

In this note we establish the regularity and uniqueness for the three-dimensional incompressible damped Boussinesq equations with zero thermal diffusion.

A numerical method based on extended Raviart–Thomas (ER‐T) mixed finite element method for solving damped Boussinesq equation

In this paper, we present the approximate solution of damped Boussinesq equation using extended Raviart–Thomas mixed finite element method. In this method, the numerical solution of this equation is obtained using triangular meshes. Also, for discretization in time direction, we use an implicit finite difference scheme. In addition, error estimation and stability analysis of both methods are shown. Finally, some numerical examples are considered to confirm the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.

Symmetries and conservation laws of a damped Boussinesq equation

In this work, we consider a damped equation with a time-independent source term. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. We also present some exact solutions. Conservation laws for this equation are constructed by using the multiplier method.

Dynamics for the damped Boussinesq equation with delay

This paper is concerned with the dynamical behavior of the damped Boussinesq equation containing a delay forcing term. It shows that, under suitable dissipative conditions, such a system possesses a pullback attractor and a uniform forward attractor in [Formula: see text].

Well-posedness and decay property for the generalized damped Boussinesq equation with double rotational inertia

Well-posedness and decay property for the generalized damped Boussinesq equation with double rotational inertia

On double reductions from symmetries and conservation laws for a damped Boussinesq equation

In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. Some nontrivial conservation laws are derived by using the multipliers method. Taking into account the relationship between symmetries and conservation laws and applying the double reduction method, we obtain a direct reduction of order of the ordinary differential equations and in particular a kink solution.

On the Cauchy problem for one dimension generalized Boussinesq equation

In this paper, we study the Cauchy problem for one dimension generalized damped Boussinesq equation. First, global existence and decay estimate of solutions to this problem are established. Second, according to the detail analysis for solution operator the generalized damped Boussinesq equation, the nonlinear approximation to global solutions is established. Finally, we prove that the global solution u to our problem is asymptotic to the superposition of nonlinear diffusion waves expressed in terms of the self-similar solution of the viscous Burgers equation as time tends to infinity.

Decay estimate of solutions to the sixth order damped Boussinesq equation

In this paper, we consider the initial value problem for the sixth order damped Boussinesq equation. We prove the global existence and asymptotic behavior of solutions for all space dimensions n⩾1 provided that the initial value is suitably small. Moreover, we show that the solution can be approximated by the linear solution as time tends to infinity for n⩾2. The result slightly improves the result obtained by Wang (2012) [3].

Asymptotic behavior for the singularly perturbed damped Boussinesq equation

This work is focused on the long-time behavior of solutions to the singularly perturbed damped Boussinesq equation in a 3D case where e > 0 is small enough. Without any growth restrictions on the nonlinearity f(u), we establish in an appropriate bounded phase space a finite dimensional global attractor as well as an exponential attractor of optimal regularity. The key step is the estimate of the difference between the solutions of the damped Boussinesq equation and the corresponding pseudo-parabolic equation.Copyright © 2014 John Wiley & Sons, Ltd.

Asymptotic behavior for the damped Boussinesq equation with critical nonlinearity

This work is focused on the long-time behavior of solutions to the damped Boussinesq equation u t t + Δ 2 u − Δ u t − Δ f ( u ) = g ( x ) , in Ω ⊂ R 3 , which describes the small nonlinear oscillations of elastic membranes in the presence of viscosity. The existence of the global attractor of optimal regularity and an exponential attractor are respectively established in the critical case.

Global Existence and Asymptotic Behavior of Solutions to the Generalized Damped Boussinesq Equation

We investigate the Cauchy problem for the generalized damped Boussinesq equation. Under small condition on the initial value, we prove the global existence and optimal decay estimate of solutions for all space dimensionsn≥1. Moreover, whenn≥2, we show that the solution can be approximated by the linear solution as time tends to infinity.

Longtime dynamics of the damped Boussinesq equation

The paper studies the longtime dynamics of the damped Boussinesq equation utt+Δ2u−Δut−Δg(u)=f(x). First, the existence of global solutions to the initial boundary value problem of the equation is obtained provided that the growth exponent of g(u), say p, is either non-supercritical (subcritical and critical) or supercritical, especially, the stability of solutions is established when p is non-supercritical. Second, the existence of a global attractor and an exponential attractor for the related solution semigroup S(t) are respectively established in the non-supercritical case.

The Asymptotic Solution of the Initial Boundary Value Problem to a Generalized Boussinesq Equation

The L2 space solution of an initial boundary problem for a generalized damped Boussinesq equation is constructed. Certain assumptions on the coefficients of the equation are found to show the existence and uniqueness of the global solution to the initial boundary problem. The explicit expression for the large time asymptotic solution is obtained.