Global Solutions to a Reactive Boussinesq System with Front Data on an Infinite Domain

1998 ◽  
Vol 193 (2) ◽  
pp. 287-316 ◽  
Author(s):  
Simon Malham ◽  
Jack X. Xin
2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana

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.


Author(s):  
Ajay Bhushan Prasad

21<sup>st</sup> Century is an era of stress and burnout. For the past few decades it has been a burning and hot topic of discussion for researchers, to evolve stress and burnout- from a global problem to global solutions, as it affects the life of individuals in an unprecedented manner and touches them at workplace across the globe. Everybody knows what stress is all about. It has become a part of life and perhaps, to some extent, necessary at work and outside work. Some people are more productive and creative when they work under stress. But if stress is intense and continuous, then it becomes a negative phenomenon leading to physical illness and psychological disorders. Stress and burnout in today's environment has become a well documented problem. Various researches have evaluated stress and burnout in workplaces. Stress is a non-specific response of body to any demand made on it. Many researchers have identified that stress and burnout has become an integral part of our daily life due to the negative aspects of job, such as, multiple responsibilities, disciplinary problems, employee's apathy, involuntary transfers, inadequate pay and perks, less chances of career advancement and lack of administrative support etc. As a result of these, individuals are likely to suffer from stress and may experience a sense of tiredness and frustration. When prolonged stress continues and it is not effectively managed, it can even lead to symptoms of burnout, a state of emotional exhaustion, depersonalization and diminished personal accomplishment in the workplace. Stress management can be done through six zones which we have discussed in detail, with a holistic approach. It includes health zone, intimate zone, family zone, work zone, social zone and spiritual zone. In this paper, an effort is made to discuss the solutions of stress and burnout in different and innovative ways through different zones which have been experienced by the author in his 20 years of professional career. Thus, stress and burnout are not a trivial problem but a major dysfunction of the 21<sup>st</sup> century, which has far reaching impact on quality and quantity of productivity. The present paper explores the concept of stress and burnout, the major differences between them, factors leading to genesis of the problem, various symptoms and how it is a serious quality concern for all professionals. Appropriate interventions for prevention and management of stress and burnout are also suggested.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Irena Lasiecka ◽  
Buddhika Priyasad ◽  
Roberto Triggiani

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.


Sign in / Sign up

Export Citation Format

Share Document