Variational analysis of 2D steady Boussinesq system

2021 ◽  
Author(s):  
Daomin Cao ◽  
Jie Wan ◽  
Weicheng Zhan
Keyword(s):  
Variational Analysis ◽  
Boussinesq System

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

scholarly journals Recent development in nonlinear and variational analysis and optimization

Optimization ◽  
2021 ◽  
Vol 70 (4) ◽  
pp. 689-692
Author(s):  
Elisabeth Köbis ◽  
Jinlu Li ◽  
Adrian Petruşel ◽  
Jen-Chih Yao
Keyword(s):  
Variational Analysis ◽  
Variational Analysis And Optimization

scholarly journals Finite-dimensional boundary uniform stabilization of the Boussinesq system in Besov spaces by critical use of Carleman estimate-based inverse theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Irena Lasiecka ◽  
Buddhika Priyasad ◽  
Roberto Triggiani
Keyword(s):  
Besov Space ◽  
Internal Control ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Critical Role ◽  
Boussinesq System ◽  
Heat Equations ◽  
Fluid Equation ◽  
Low Regularity ◽  
Finite Dimensional

Abstract We consider the 𝑑-dimensional Boussinesq system defined on a sufficiently smooth bounded domain and subject to a pair { v , u } \{v,\boldsymbol{u}\} of controls localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . Here, 𝑣 is a scalar Dirichlet boundary control for the thermal equation, acting on an arbitrarily small connected portion Γ ~ \widetilde{\Gamma} of the boundary Γ = ∂ ⁡ Ω \Gamma=\partial\Omega . Instead, 𝒖 is a 𝑑-dimensional internal control for the fluid equation acting on an arbitrarily small collar 𝜔 supported by Γ ~ \widetilde{\Gamma} . The initial conditions for both fluid and heat equations are taken of low regularity. We then seek to uniformly stabilize such Boussinesq system in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of an explicitly constructed, finite-dimensional feedback control pair { v , u } \{v,\boldsymbol{u}\} localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . In addition, they will be minimal in number and of reduced dimension; more precisely, 𝒖 will be of dimension ( d - 1 ) (d-1) , to include necessarily its 𝑑-th component, and 𝑣 will be of dimension 1. The resulting space of well-posedness and stabilization is a suitable, tight Besov space for the fluid velocity component (close to L 3 ⁢ ( Ω ) \boldsymbol{L}^{3}(\Omega) for d = 3 d=3 ) and a corresponding Besov space for the thermal component, q > d q>d . Unique continuation inverse theorems for suitably over-determined adjoint static problems play a critical role in the constructive solution. Their proof rests on Carleman-type estimates, a topic pioneered by M. V. Klibanov since the early 80s.

Prediction of a Billet Shape for Axisymmetric Warm Forming Using Variational Analysis

2004 ◽  
Vol 274-276 ◽  
pp. 733-738 ◽  
Author(s):  
Ting Fai Kong ◽  
Luen Chow Chan ◽  
Tai Chiu Lee
Keyword(s):  
Variational Analysis ◽  
Warm Forming ◽  
Billet Shape

scholarly journals Variational analysis of HF dimer tunneling rotational spectra using an ab initio potential energy surface

2021 ◽  
pp. 111481
Author(s):  
Oleg L. Polyansky ◽  
Roman I. Ovsyannikov ◽  
Jonathan Tennyson ◽  
Sergei P. Belov ◽  
Mikhail Yu. Tretyakov ◽  
...  
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Variational Analysis ◽  
Energy Surface ◽  
Rotational Spectra

scholarly journals The linearized classical Boussinesq system on the half‐line

2021 ◽  
Vol 146 (3) ◽  
pp. 635-657
Author(s):  
C. M. Johnston ◽  
Clarence T. Gartman ◽  
Dionyssios Mantzavinos
Keyword(s):  
Boussinesq System ◽  
Half Line
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