Analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations arising in the flow and heat transfer of a viscoelastic,...Analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations arising in the flow and heat transfer of a viscoelastic, electrically conducting fluid past a continuously stretching sheet. The ranges of the parametric values are obtained for which the system has a unique pair of solutions, a double pair of solutions and infinitely many solutions.展开更多
In this paper we discuss the uniqueness and existence of solution to a real gas flow network by employing graph theory. A directed graph is an efficient way to represent a gas network. We consider steady state real ga...In this paper we discuss the uniqueness and existence of solution to a real gas flow network by employing graph theory. A directed graph is an efficient way to represent a gas network. We consider steady state real gas flow network that includes pipelines, compressors, and the connectors. The pipelines and compressors are represented as edges of the graph and the interconnecting points are represented as nodes of the graph representing the network. We show that a unique solution of such a system exists. We use monotonicity property of a mapping to proof uniqueness, and the contraction mapping theorem is used to prove existence.展开更多
In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic...In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.展开更多
The existence and uniqueness of a strong periodic solution of the evolution system describing geophysical flow in bounded domains of RN (N = 3, 4) are proven if external forces are periodic in time and sufficiently sm...The existence and uniqueness of a strong periodic solution of the evolution system describing geophysical flow in bounded domains of RN (N = 3, 4) are proven if external forces are periodic in time and sufficiently small.展开更多
The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvatu...The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.展开更多
To solve nonlinear system of equation,F(x) = 0,a continuous Newton flow x_t(t) = V(x) =-(DF(x))^(-1)F(x),x(0) =x^0 and its mathematical properties,such as the central field,global existence and uniqueness of real root...To solve nonlinear system of equation,F(x) = 0,a continuous Newton flow x_t(t) = V(x) =-(DF(x))^(-1)F(x),x(0) =x^0 and its mathematical properties,such as the central field,global existence and uniqueness of real roots and the structure of the singular surface,are studied.We concisely introduce random Newton flow algorithm(NFA) for finding all roots,based on discrete Newton flow x^(j+1)=x^j+hV{x^j) with random initial value x^0 and h∈(0,1],and three computable quantities,g_j,d_j and K_j.The numerical experiments with dimension n=300 are provided.展开更多
文摘Analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations arising in the flow and heat transfer of a viscoelastic, electrically conducting fluid past a continuously stretching sheet. The ranges of the parametric values are obtained for which the system has a unique pair of solutions, a double pair of solutions and infinitely many solutions.
文摘In this paper we discuss the uniqueness and existence of solution to a real gas flow network by employing graph theory. A directed graph is an efficient way to represent a gas network. We consider steady state real gas flow network that includes pipelines, compressors, and the connectors. The pipelines and compressors are represented as edges of the graph and the interconnecting points are represented as nodes of the graph representing the network. We show that a unique solution of such a system exists. We use monotonicity property of a mapping to proof uniqueness, and the contraction mapping theorem is used to prove existence.
文摘In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.
基金the Special Funds for Major State Basic Research Projects of China(No.G1999032801) and the National Natural Science Foundation
文摘The existence and uniqueness of a strong periodic solution of the evolution system describing geophysical flow in bounded domains of RN (N = 3, 4) are proven if external forces are periodic in time and sufficiently small.
文摘The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.
基金National Natural Science Foundation of China(Grant Nos. 11301176,11071067 and 11226332)
文摘To solve nonlinear system of equation,F(x) = 0,a continuous Newton flow x_t(t) = V(x) =-(DF(x))^(-1)F(x),x(0) =x^0 and its mathematical properties,such as the central field,global existence and uniqueness of real roots and the structure of the singular surface,are studied.We concisely introduce random Newton flow algorithm(NFA) for finding all roots,based on discrete Newton flow x^(j+1)=x^j+hV{x^j) with random initial value x^0 and h∈(0,1],and three computable quantities,g_j,d_j and K_j.The numerical experiments with dimension n=300 are provided.
