In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanizati...A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment.展开更多
In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
In this paper, some sufficient conditions for the oscillation for solutions to systems of n-th order partial functional differential equations are obtained.
In this paper, we investigate optimal policies for an age-dependent n-dimensional competition system, which is controlled by fertility. By using Dubovitskii-Milyutin＇s general theory, the maximum principles are obtai...In this paper, we investigate optimal policies for an age-dependent n-dimensional competition system, which is controlled by fertility. By using Dubovitskii-Milyutin＇s general theory, the maximum principles are obtained for the problems with free terminal states, infinite horizon, and target sets, respectively.展开更多
In this note, we consider a Fremond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and extern...In this note, we consider a Fremond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we generalize the paper dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor.展开更多
Time-dependent viscous fluid flow due to a stretchable rotating disk is investigated.Magnetic field is applied in vertical direction to the disk.Temperature equation is assisted with Joule heating effect.Governing sys...Time-dependent viscous fluid flow due to a stretchable rotating disk is investigated.Magnetic field is applied in vertical direction to the disk.Temperature equation is assisted with Joule heating effect.Governing system of PDE's is transformed to dimensionless form by suitable variables.One of the numerical techniques known as finite difference scheme is adopted to tackle the given dimensionless partial differential system.This method results in a system of simple algebraic equations.The unknown function is analyzed inside domain of interest.In this technique of solution,a system is subdivided into many smaller parts called finite elements.The obtained simpler algebraic equations are then assembled to form a system of equations which governs the original problem.Variational method is used to get approximate solution by reducing the error function.Behaviors of pertinent variables on surface drag force,temperature,velocity and heat transfer rate are shown graphically.The obtained outcomes guarantee that velocity decreases for Hartmann number while it enhances with Reynolds number.Temperature increases for higher Prandtl,Eckert and Hartmann numbers.Skin friction boosts for larger values of Hartmann number.Nusselt number enhances with Hartmann number.展开更多
This paper presents a fractional approach to study the mathematical model of tsunami wave propagation along a coastline of an ocean.Fractional Reduced Differential Transform Method(FRDTM)is used to analyze this model....This paper presents a fractional approach to study the mathematical model of tsunami wave propagation along a coastline of an ocean.Fractional Reduced Differential Transform Method(FRDTM)is used to analyze this model.The present model has been studied on the shallow-water assumption.It is represented by a time-fractional coupled system of non-linear partial differential equations.Solutions to the proposed model for different coastal slopes and ocean depths have been obtained.Effects of coast slope and sea depth variations on tsunami wave velocity and wave amplification have been demonstrated at different time levels and different ordersα.The obtained results are compared with Elzaki Adomian Decomposition Method(EADM)to validate the proposed method for an orderα=1.展开更多
文摘In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
文摘A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment.
文摘In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
文摘In this paper, some sufficient conditions for the oscillation for solutions to systems of n-th order partial functional differential equations are obtained.
基金The work is supported by‘Qing Lan’Talent Engineering Funds(QL-05-1SA) by Lanzhou Jiaotong Universitythe National Natural Science Foundation of China under Grant No.604730304.
文摘In this paper, we investigate optimal policies for an age-dependent n-dimensional competition system, which is controlled by fertility. By using Dubovitskii-Milyutin＇s general theory, the maximum principles are obtained for the problems with free terminal states, infinite horizon, and target sets, respectively.
基金Project supported by the MIUR-COFIN 2004 research program on "Mathematical Modelling and Analysis of Free Boundary Problems".
文摘In this note, we consider a Fremond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we generalize the paper dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor.
文摘Time-dependent viscous fluid flow due to a stretchable rotating disk is investigated.Magnetic field is applied in vertical direction to the disk.Temperature equation is assisted with Joule heating effect.Governing system of PDE's is transformed to dimensionless form by suitable variables.One of the numerical techniques known as finite difference scheme is adopted to tackle the given dimensionless partial differential system.This method results in a system of simple algebraic equations.The unknown function is analyzed inside domain of interest.In this technique of solution,a system is subdivided into many smaller parts called finite elements.The obtained simpler algebraic equations are then assembled to form a system of equations which governs the original problem.Variational method is used to get approximate solution by reducing the error function.Behaviors of pertinent variables on surface drag force,temperature,velocity and heat transfer rate are shown graphically.The obtained outcomes guarantee that velocity decreases for Hartmann number while it enhances with Reynolds number.Temperature increases for higher Prandtl,Eckert and Hartmann numbers.Skin friction boosts for larger values of Hartmann number.Nusselt number enhances with Hartmann number.
文摘This paper presents a fractional approach to study the mathematical model of tsunami wave propagation along a coastline of an ocean.Fractional Reduced Differential Transform Method(FRDTM)is used to analyze this model.The present model has been studied on the shallow-water assumption.It is represented by a time-fractional coupled system of non-linear partial differential equations.Solutions to the proposed model for different coastal slopes and ocean depths have been obtained.Effects of coast slope and sea depth variations on tsunami wave velocity and wave amplification have been demonstrated at different time levels and different ordersα.The obtained results are compared with Elzaki Adomian Decomposition Method(EADM)to validate the proposed method for an orderα=1.
