To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem...To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.展开更多
In this paper, sane 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 are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differen...In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated.Sufficient conditions for oscillations of such equations are obtained.展开更多
In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish...In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.展开更多
In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and D...In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet＇s boundary value conditions.展开更多
In this article, we will establish sufficient conditions for the interval oscillation of fractional partial differential equations of the form It is based on the information only on a sequence of subintervals of the t...In this article, we will establish sufficient conditions for the interval oscillation of fractional partial differential equations of the form It is based on the information only on a sequence of subintervals of the time space rather than whole half line. We consider f to be monotonous and non monotonous. By using a generalized Riccati technique, integral averaging method, Philos type kernals and new interval oscillation criteria are established. We also present some examples to illustrate our main results.展开更多
An L-stable block method based on hybrid second derivative algorithm (BHSDA) is provided by a continuous second derivative method that is defined for all values of the independent variable and applied to parabolic par...An L-stable block method based on hybrid second derivative algorithm (BHSDA) is provided by a continuous second derivative method that is defined for all values of the independent variable and applied to parabolic partial differential equations (PDEs). The use of the BHSDA to solve PDEs is facilitated by the method of lines which involves making an approximation to the space derivatives, and hence reducing the problem to that of solving a time-dependent system of first order initial value ordinary differential equations. The stability properties of the method is examined and some numerical results presented.展开更多
We consider the oscillation of a class fractional differential equation with Robin and Dirichlet boundary conditions. By generalized Riccati transformation technique and the differential inequality method, oscillation...We consider the oscillation of a class fractional differential equation with Robin and Dirichlet boundary conditions. By generalized Riccati transformation technique and the differential inequality method, oscillation criteria for a class of nonlinear fractional differential equation are obtained.展开更多
In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions fo...In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.展开更多
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, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local trunc...In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.展开更多
In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular ...In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h2).展开更多
In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j...In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.展开更多
In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation ar...In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.展开更多
In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we es...In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we establish some sufficient criteria with respect to the oscillations of such systems, employing first-order impulsive delay differential inequalities. The results fully reflect the influence action of impulsive and delay in oscillation.展开更多
This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations,...This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations, and these results are illustrated by some examples.展开更多
In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and...In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and the technique of differential inequalities, some new sufficient conditions are obtained for the oscillation of the partial differential equations under Robin boundary value conditions. The results generalize some of the previous results.展开更多
Sufficient conditions are obtained for the oscillation of the solutions to nonlinear parabolic differential equations of neutral type in the form of where Ω is a bounded domain in Rn with a piecewise smooth boundary.
Recently, Kreith, Kusano and Yoshida have studied the oscillation property of the hyperbolic equation u<sub>11</sub>-△u+c（t,x,u）=f（t,x）, （t,x）∈R<sub>+</sub>×Ωwith boundary conditi...Recently, Kreith, Kusano and Yoshida have studied the oscillation property of the hyperbolic equation u<sub>11</sub>-△u+c（t,x,u）=f（t,x）, （t,x）∈R<sub>+</sub>×Ωwith boundary condition （?）u/（?）n=g（t,x）, （t, x）∈R<sub>+</sub>×（?）Ω,and obtained some sufficient criterions for solution oscillation. In this note, we shall discuss the oscillation properties of solutions for a class of hyperbolic functional differential展开更多
文摘To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.
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In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
基金Supported by the Natural Science Foundation of China(10471086)Supported by the Science Research Foundation of Department of Education of Hunan Province(07C164)
文摘In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated.Sufficient conditions for oscillations of such equations are obtained.
文摘In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.
基金the Natural Science Foundation of Hunan Province(10471086)the Science Research Foundation of Administration of Education of Hunan Province(07C164)
文摘In this paper, some sufficient conditions are obtained for the oscillation of solutions for a class of second order nonlinear neutral partial differential equations with continuous distribution delay under Robin and Dirichlet＇s boundary value conditions.
文摘In this article, we will establish sufficient conditions for the interval oscillation of fractional partial differential equations of the form It is based on the information only on a sequence of subintervals of the time space rather than whole half line. We consider f to be monotonous and non monotonous. By using a generalized Riccati technique, integral averaging method, Philos type kernals and new interval oscillation criteria are established. We also present some examples to illustrate our main results.
文摘An L-stable block method based on hybrid second derivative algorithm (BHSDA) is provided by a continuous second derivative method that is defined for all values of the independent variable and applied to parabolic partial differential equations (PDEs). The use of the BHSDA to solve PDEs is facilitated by the method of lines which involves making an approximation to the space derivatives, and hence reducing the problem to that of solving a time-dependent system of first order initial value ordinary differential equations. The stability properties of the method is examined and some numerical results presented.
文摘We consider the oscillation of a class fractional differential equation with Robin and Dirichlet boundary conditions. By generalized Riccati transformation technique and the differential inequality method, oscillation criteria for a class of nonlinear fractional differential equation are obtained.
基金Supported by the National Natural Science Foundation of China(10471086).
文摘In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.
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.
文摘In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.
基金This work is supported by the National Fujian Province Nature Science Research Funds
文摘In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h2).
基金Supported by the National Natural Science Foundation of China
文摘In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.
基金This work is supported by National Natural Science Foundation of China (40373003 and 40372121).
文摘In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.
基金the Natural Science Foundation of Hunan Province under Grant 05JJ40008.
文摘In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we establish some sufficient criteria with respect to the oscillations of such systems, employing first-order impulsive delay differential inequalities. The results fully reflect the influence action of impulsive and delay in oscillation.
基金Supported by Natural Science Foundation of Hebei Province（102160） and Natural Science of Education office in Hebei Province （2004123）,
文摘This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations, and these results are illustrated by some examples.
基金Supported by Guangdong Province Teaching Reform Project in Higher Education(GDJG20142396)Higher School Characteristic Innovation Project(research in education)of Guangdong Province in 2014
文摘In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and the technique of differential inequalities, some new sufficient conditions are obtained for the oscillation of the partial differential equations under Robin boundary value conditions. The results generalize some of the previous results.
文摘Sufficient conditions are obtained for the oscillation of the solutions to nonlinear parabolic differential equations of neutral type in the form of where Ω is a bounded domain in Rn with a piecewise smooth boundary.
文摘Recently, Kreith, Kusano and Yoshida have studied the oscillation property of the hyperbolic equation u<sub>11</sub>-△u+c（t,x,u）=f（t,x）, （t,x）∈R<sub>+</sub>×Ωwith boundary condition （?）u/（?）n=g（t,x）, （t, x）∈R<sub>+</sub>×（?）Ω,and obtained some sufficient criterions for solution oscillation. In this note, we shall discuss the oscillation properties of solutions for a class of hyperbolic functional differential
