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Rayleigh-type wave propagation through liquid layer over corrugated substrate

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Applied mathematics and Mechanics(English Edition) 2017年第6期38卷 851-866页

作者： A.K.SINGH A.DAS A.RAY Department of Applied mathematics Indian Institute of Technology(ISM)

The propagation of the Rayleigh-type wave in a fluid layer overlying a corrugated substrate is studied. The corrugated substrate is considered as a fluid satu- rated poroelastic substrate and a quadratically heterogeneous isotropic elastic substrate in Case I and Case II, respectively. Closed form expressions of dispersion relation for Case I and Case II ave obtained. The influence of corrugation, porosity, and hetero- geneity on the phase velocity of Rayleigh-type wave, for both cases, is highlighted and demonstrated through numerical computation and graphical discussion. Neglecting cor- rugation at the common interface, expressions of phase velocity of the Rayleigh-type wave for both cases ave derived in a closed form as a special case of the problem. Comparison between the presence and the absence of both heterogeneity and poroelasticity in the substrate of the composite structure is a key in the present study.

关键词： Rayleigh-type wave porosity heterogeneity corrugation

ON SOLUTION TO THE NAVIER-STOKES EQUATIONS WITH NAVIER SLIP BOUNDARY CONDITION FOR THREE DIMENSIONAL INCOMPRESSIBLE FLUID

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Acta Mathematica Scientia 2019年第6期39卷 1628-1638页

作者： Subha PAL Rajib HALOI Department of Mathematical Sciences Tezpur University

In this article, we prove the existence and uniqueness of solutions of the NavierStokes equations with Navier slip boundary condition for incompressible fluid in a bounded domain of R^3. The results are established by... 详细信息

关键词： Navier-Stokes equations Galerkin method Navier slip boundary condition strain tensor

Augmented Lyapunov approach to H_∞ state estimation of static neural networks with discrete and distributed time-varying delays

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Chinese Physics B 2015年第5期24卷 140-147页

作者： M.Syed Ali R.Saravanakumar Department of mathematics Thiruvalluvar University

This paper deals with H∞ state estimation problem of neural networks with discrete and distributed time-varying delays. A novel delay-dependent concept of H∞ state estimation is proposed to estimate the H∞ performance and global asymptotic stability of the concerned neural networks. By constructing the Lyapunov-Krasovskii functional and using the linear matrix inequality technique, sufficient conditions for delay-dependent H∞ performances are obtained, which can be easily solved by some standard numerical algorithms. Finally, numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results.

关键词： distributed delay H∞ state estimation neural networks stability analysis

Nonsmooth Semi-Infinite Minmax Programming Involving Generalized(Φ, ρ)-Invexity

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Journal of Systems Science & Complexity 2015年第4期28卷 857-875页

作者： UPADHYAY B B MISHRA S K Department of Basic Sciences & Humanities National Institute of Technology

This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the necessary and sufficient optimality conditions for a class of nonsmooth semi-infinite minmax programming problems, where set of restrictions are indexed in a compact set. Utilizing the sufficient optimality conditions, the authors formulate three types of dual models and establish weak and strong duality results. The results of the paper extend and unify naturally some earlier results from the literature.

关键词： Duality, generalized invexity locally Lipschitz functions, minmax programming, semi-infinite programming.

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

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Journal of Systems Science & Complexity 2015年第5期28卷 1033-1048页

作者： PALANISAMY Muthukumar CHINNATHAMBI Rajivganthi Department of mathematics Gandhigram Rural Institute-Deemed University

The modelling of risky asset by stochastic processes with continuous paths, based on Brownian motions, suffers from several defects. First, the path continuity assumption does not seem reasonable in view of the possibility of sudden price variations(jumps) resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

关键词： Approximate controllability Hilbert space Poisson jumps second-order neutral stochastic differential equations semigroup theory

Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet

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Chinese Physics B 2014年第12期23卷 289-292页

作者： Krishnendu Bhattacharyya Tasawar Hayat Ahmed Alsaedi Department of mathematics The University of Burdwan Department of mathematics Quaid-I-Azam University Department of mathematics Faculty of Science King Abdulaziz University

An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.

关键词： dual solutions boundary layer flow Maxwell fluid porous shrinking sheet

A Multilevel Domain Decomposition Approach for Studying Coupled Flow Applications

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Communications in Computational Physics 2009年第7期6卷 319-341页

作者： E.Aulisa A.Cervone S.Manservisi P.Seshaiyer Department of mathematics and Statistics Texas Tech UniversityLubbockTX 79409-1042USA Laboratory of Montecuccolino DIENCAUniversity of BolognaBologna40136Italy Department of Mathematical Sciences George Mason UniversityFairfaxVA 22030USA

In this paper,a multilevel domain decomposition approach based on multigrid methods for obtaining fast solutions for coupled engineering flow applications arising on complex domains is *** proposed technique not only allows solutions to be computed efficiently at the element level but also helps us to achieve proper accuracy,load balancing and computational *** results presented demonstrate the robustness of the proposed technique.

关键词： Finiteelementmethods multigridmethods domaindecomposition

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

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Acta Mathematica Scientia 2014年第5期34卷 1461-1472页

作者： Manoj K.YADAV Department of mathematics Indian Institute of Science

In this article, we obtain explicit solutions of a linear PDE subject to a class of ra-dial square integrable functions with a monotonically increasing weight function｜x｜n-1eβ｜x｜2/2,β ≥ 0, x ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n＆gt;1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.

关键词： forced Burgers equation radial Hermite functions generalized Laguerre poly-nomials self-similar solutions

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

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Journal of Systems Engineering and Electronics 2015年第5期26卷 1033-1048页

作者： PALANISAMY Muthukumar CHINNATHAMBI Rajivganthi Department of mathematics Gandhigram Rural Institute-Deemed University

The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

关键词： Approximate controllability Hilbert space Poisson jumps second-order neutral stochas-tic differential equations semigroup theory.