This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive...This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.展开更多
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations....In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.展开更多
The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coeffic...The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coefficient D = 0 and the solution blows up ifD= 0. The method of linearization is applied to derive the existence of Hopfs bifurcation which is the signature of instability of Turing system. The increasing of the size of the attractor and the existence of Hopf＇ s bifurcation indicate that there is a threshold that initiates the instability.展开更多
In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transf...In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to （2＋1）-dimensionM dispersive long wave equation and successfully obtain many new doubly periodic solutions. When the modulus m→1, these sohitions degenerate as soliton solutions. The method can be also applied to other nonlinear partial differential equations.展开更多
In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of...In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of the underlying processes, we show that if dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null in distribution and if βd > 2, then Xt will converge to a nondegenerative random measure in the same sense.展开更多
In this paper a finite element model is developed to study cytosolic calcium concen- tration distribution in astrocytes for a two-dimensional steady-state case in presence of excess buffer. The mathematical model of c...In this paper a finite element model is developed to study cytosolic calcium concen- tration distribution in astrocytes for a two-dimensional steady-state case in presence of excess buffer. The mathematical model of calcium diffusion in astrocytes leads to a boundary value problem involving elliptical partial differential equation. The model con- sists of reaction-diffusion phenomena, association and dissociation rates and buffer. A point source of calcium is incorporated in the model. Appropriate boundary conditions have been framed. Finite element method is employed to solve the problem. A MATLAB program has been developed for the entire problem and simulated to compute the numer- ical results. The numerical results have been used to plot calcium concentration profiles in astrocytes. The effect of ECTA, BAPTA and aCa influx on calcium concentration distribution in astrocytes is studied with the help of numerical results.展开更多
文摘This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.
文摘In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
文摘The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coefficient D = 0 and the solution blows up ifD= 0. The method of linearization is applied to derive the existence of Hopfs bifurcation which is the signature of instability of Turing system. The increasing of the size of the attractor and the existence of Hopf＇ s bifurcation indicate that there is a threshold that initiates the instability.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004 CB 318000
文摘In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to （2＋1）-dimensionM dispersive long wave equation and successfully obtain many new doubly periodic solutions. When the modulus m→1, these sohitions degenerate as soliton solutions. The method can be also applied to other nonlinear partial differential equations.
文摘In this paper, we investigate super-uniformly elliptic diffusions {Xt,t ≥ 0} with its branching mechanism given by ψ(z) = γz1+β(0 < ≤ 1), and, when the initial value X0(dx) is one kind of invariant measures of the underlying processes, we show that if dimension d satisfies βd ≤ 2, then the random measures Xt will converge to the null in distribution and if βd > 2, then Xt will converge to a nondegenerative random measure in the same sense.
文摘In this paper a finite element model is developed to study cytosolic calcium concen- tration distribution in astrocytes for a two-dimensional steady-state case in presence of excess buffer. The mathematical model of calcium diffusion in astrocytes leads to a boundary value problem involving elliptical partial differential equation. The model con- sists of reaction-diffusion phenomena, association and dissociation rates and buffer. A point source of calcium is incorporated in the model. Appropriate boundary conditions have been framed. Finite element method is employed to solve the problem. A MATLAB program has been developed for the entire problem and simulated to compute the numer- ical results. The numerical results have been used to plot calcium concentration profiles in astrocytes. The effect of ECTA, BAPTA and aCa influx on calcium concentration distribution in astrocytes is studied with the help of numerical results.
