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Initial Value Problem of Singular n-Laplacian Equation
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作者 王宏洲 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2001年第3期225-232,共8页
To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems... To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems with n Laplacian operators are established in three singular cases. 展开更多
关键词 initial value problem n Laplacian operator positive solution CONE
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Solution Method for Singular Initial Value Problems of One-dimensional Steady Transonic Flow in a Dual-mode Scramjet 被引量:1
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作者 崔涛 于达仁 鲍文 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2005年第2期97-101,共5页
Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts f... Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts forward an improved algorithm based on variable transformation, and constructs a nonsingular one-dimensional steady transonic flow equation by defining a new variable. The improved algorithm can eliminate the singularity of the differential equation, and can solve the singular initial value problems of one-dimensional steady transonic flow of dual-mode scramjet. 展开更多
关键词 SCRAMJET one-dimensional analysis transonic flow singular initial value problem
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Initial value problem for a class of fourth-order nonlinear wave equations 被引量:1
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作者 陈国旺 侯长顺 Shi-qiang DAI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第3期391-401,共11页
In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractio... In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given. 展开更多
关键词 fourth-order nonlinear wave equation initial value problem global solution blow up of solution
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Laguerre-Gauss collocation method for initial value problems of second order ODEs 被引量:1
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作者 严建平 郭本瑜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第12期1541-1564,共24页
This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. N... This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency. 展开更多
关键词 Laguerre-Gauss collocation method initial value problem second orderODEs
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Numerical Treatment of Initial Value Problems of Nonlinear Ordinary Differential Equations by Duan-Rach-Wazwaz Modified Adomian Decomposition Method 被引量:1
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作者 Omür Umut Serpil Yasar 《International Journal of Modern Nonlinear Theory and Application》 2019年第1期17-39,共23页
We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robus... We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robustness and reliability of the method, we compare the results from the modified Adomian decomposition method with those from the MATHEMATICA solutions and also from the fourth-order Runge Kutta method solutions in some cases. Furthermore, we apply Padé approximants technique to improve the solutions of the modified decomposition method whenever the exact solutions exist. 展开更多
关键词 Adomian Decomposition Method Duan-Rach-Wazwaz Modified Adomian Decomposition Method initial value problem Nonlinear Ordinary Differential Equation Mathematica Solution 4-th Order Runge Kutta Method Pade Approximants
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THE STABILITY ON THE SOLUTION OF THE INITIAL VALUE PROBLEM
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作者 邵孝湟 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第10期1001-1008,共8页
In this paper, using the differentiability of the solution with respect to the initial value and the parameter, we present a method which, different from Liapunov's direct method. will determine the stability oj t... In this paper, using the differentiability of the solution with respect to the initial value and the parameter, we present a method which, different from Liapunov's direct method. will determine the stability oj the non-stationary solution of the initial value problem when the non-stationary solution remains unknown. 展开更多
关键词 STABILITY initial value problem DIFFERENTIABILITY
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Discretized Multisplitting AOR Waveform Relaxation Algorithms for Initial Value Problem of Systems of ODEs
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作者 谷同祥 李文强 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第4期27-35, ,共9页
The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in [1]. On fixed time intervals conver gence results could be derived ... The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in [1]. On fixed time intervals conver gence results could be derived if the subsystems are solving exactly.Firstly,in theis paper,we deal with an extension of the waveform relaxation algorithm by us ing multisplittin AOR method based on an overlapping block decomposition. We restricted our selves to equidistant timepoints and dealed with the case that an implicit integration method was used to solve the subsystems numerically in parallel. Then we have proved convergence of multi splitting AOR waveform relaxation algorithm on a fixed window containing a finite number of timepoints. 展开更多
关键词 systems of ordinary differential equations initial value problems multisplitting algorithm AOR method waveform relaxation algorithm
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Initial Value Problems for Second Order Impulsive Integro-Differential Equation in Banach Spaces
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作者 陈芳启 张海燕 《Transactions of Tianjin University》 EI CAS 2005年第1期73-78,共6页
By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differenti... By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differential equation in Banach spaces is obtained and the related results are essentially improved.At the same time, another sufficient condition of existence of minimal and maximal solutions based on the Kuratowski measure of noncompactness is given. 展开更多
关键词 impulsive integro-differential equation initial value problem comparison result
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An Explicit Single-Step Nonlinear Numerical Method for First Order Initial Value Problems (IVPs)
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作者 Omolara Fatimah Bakre Ashiribo Senapon Wusu Moses Adebowale Akanbi 《Journal of Applied Mathematics and Physics》 2020年第9期1729-1735,共7页
Interest in the construction of efficient methods for solving initial value problems that have some peculiar properties with it or its solution is recently gaining wide popularity. Based on the assumption that the sol... Interest in the construction of efficient methods for solving initial value problems that have some peculiar properties with it or its solution is recently gaining wide popularity. Based on the assumption that the solution is representable by nonlinear trigonometric expressions, this work presents an explicit single-step nonlinear method for solving first order initial value problems whose solution possesses singularity. The stability and convergence properties of the constructed scheme are also presented. Implementation of the new method on some standard test problems compared with those discussed in the literature proved its accuracy and efficiency. 展开更多
关键词 Ordinary Differential Equations First Order initial value problems NONLINEAR SINGULARITIES
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Perturbation by Decomposition:A New Approach to Singular Initial Value Problems with Mamadu-Njoseh Polynomials as Basis Functions
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作者 Mamadu E.J. Tsetimi J. 《Journal of Mathematics and System Science》 2020年第1期15-18,共4页
This paper focuses on the application of Mamadu-Njoseh polynomials(MNPs)as basis functions for the solution of singular initial value problems in the second-order ordinary differential equations in a perturbation by d... This paper focuses on the application of Mamadu-Njoseh polynomials(MNPs)as basis functions for the solution of singular initial value problems in the second-order ordinary differential equations in a perturbation by decomposition approach.Here,the proposed method is an hybrid of the perturbation theory and decomposition method.In this approach,the approximate solution is slihtly perturbed with the MNPs to ensure absolute convergence.Nonlinear cases are first treated by decomposition.The method is,easy to execute with well-posed mathematical formulae.The existence and convergence of the method is also presented explicitly.Resulting numerical evidences show that the proposed method,in comparison with the Adomian Decomposition Method(ADM),Homotpy Pertubation Method and the exact solution is reliable,efficient and accuarate. 展开更多
关键词 Perturbation method Orthogonal polynomials Mamadu-Njoseh polynomials Chebychev polynomials singular initial value problems ordinary differential equation(ODE)
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WELL-POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INVISCID COMPRESSIBLE ADIABATIC FLUID
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作者 王曰朋 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第7期865-871,共7页
The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some repr... The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some representative initial or boundary value problem, thus the structure of solution space for local (exact) solution of the Euler equations is determined. Moreover the computation formulas of the analytical solution of the well-posed problem are also given. 展开更多
关键词 Euler equation initial or boundary value problem WELL-POSEDNESS stratification theory
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LEGENDRE-GAUSS-RADAU SPECTRAL COLLOCATION METHOD FOR NONLINEAR SECOND-ORDER INITIAL VALUE PROBLEMS WITH APPLICATIONS TO WAVE EQUATIONS
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作者 Lina Wang Qian Tong +1 位作者 Lijun Yi Mingzhu Zhang 《Journal of Computational Mathematics》 SCIE CSCD 2024年第1期217-247,共31页
We propose and analyze a single-interval Legendre-Gauss-Radau(LGR)spectral collocation method for nonlinear second-order initial value problems of ordinary differential equations.We design an efficient iterative algor... We propose and analyze a single-interval Legendre-Gauss-Radau(LGR)spectral collocation method for nonlinear second-order initial value problems of ordinary differential equations.We design an efficient iterative algorithm and prove spectral convergence for the single-interval LGR collocation method.For more effective implementation,we propose a multi-interval LGR spectral collocation scheme,which provides us great flexibility with respect to the local time steps and local approximation degrees.Moreover,we combine the multi-interval LGR collocation method in time with the Legendre-Gauss-Lobatto collocation method in space to obtain a space-time spectral collocation approximation for nonlinear second-order evolution equations.Numerical results show that the proposed methods have high accuracy and excellent long-time stability.Numerical comparison between our methods and several commonly used methods are also provided. 展开更多
关键词 Legendre-Gauss-Radau collocation method Second-order initial value problem Spectral convergence Wave equation
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Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in R^(N)
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作者 Xingli Li Jianli Liu Manwai Yuen 《Annals of Applied Mathematics》 2024年第3期249-261,共13页
In fluid mechanics and astrophysics,relativistic Euler equations can be used to describe the effects of special relativity which are an extension of the classical Euler equations.In this paper,we will consider the ini... In fluid mechanics and astrophysics,relativistic Euler equations can be used to describe the effects of special relativity which are an extension of the classical Euler equations.In this paper,we will consider the initial value problem of relativistic Euler equations in an initial bounded region of R N.If the initial velocity satisfies max→x 0∈∂Ω(0)N∑i=1 v_(i)^(2)(0,→x 0)<c^(2)A_(1)/2,where A 1 is a positive constant depend on some sufficiently large T^(*),then we can get the non-global existence of the regular solution for the N-dimensional relativistic Euler equations. 展开更多
关键词 Non-global existence relativistic Euler equations regular solution initial value problem
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Representation of measures of noncompactness and its applications related to an initial value problem in Banach spaces 被引量:1
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作者 Xiaoling Chen Lixin Cheng 《Science China Mathematics》 SCIE CSCD 2023年第4期745-776,共32页
This paper is devoted to studying the representation of measures of non-generalized compactness,in particular,measures of noncompactness,of non-weak compactness and of non-super weak compactness,defined on Banach spac... This paper is devoted to studying the representation of measures of non-generalized compactness,in particular,measures of noncompactness,of non-weak compactness and of non-super weak compactness,defined on Banach spaces and its applications.With the aid of a three-time order-preserving embedding theorem,we show that for every Banach space X,there exist a Banach function space C(K)for some compact Hausdorff space K and an order-preserving affine mapping T from the super space B of all the nonempty bounded subsets of X endowed with the Hausdorff metric to the positive cone C(K)^(+) of C(K),such that for every convex measure,in particular,the regular measure,the homogeneous measure and the sublinear measure of non-generalized compactnessμon X,there is a convex function F on the cone V=T(B)which is Lipschitzian on each bounded set of V such that F(T(B))=μ(B),■B∈B.As its applications,we show a class of basic integral inequalities related to an initial value problem in Banach spaces,and prove a solvability result of the initial value problem,which is an extension of some classical results due to Bana′s and Goebel(1980),Goebel and Rzymowski(1970)and Rzymowski(1971). 展开更多
关键词 representation of measures of noncompactness convex analysis Lebesgue-Bochner measurability integral inequality initial value problem in Banach spaces
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Local and Global Existence of Solutions to Initial Value Problems of Modified Nonlinear Kawahara Equations 被引量:11
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作者 Shuang Ping TAO Shang Bin CUI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第5期1035-1044,共10页
This paper is devoted to studying the initial value problem of the modified nonlinear Kawahara equation the first partial dervative of u to t ,the second the third +α the second partial dervative of u to x ,the seco... This paper is devoted to studying the initial value problem of the modified nonlinear Kawahara equation the first partial dervative of u to t ,the second the third +α the second partial dervative of u to x ,the second the third +β the third partial dervative of u to x ,the second the thire +γ the fifth partial dervative of u to x = 0,(x,t)∈R^2.We first establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem. Then we apply such estimates to prove local and global existence of solutions for the initial value problem of the modified nonlinear Karahara equation. The results show that a local solution exists if the initial function uo(x) ∈ H^s(R) with s ≥ 1/4, and a global solution exists if s ≥ 2. 展开更多
关键词 Kawahara equation initial value problem SOLUTION Local existence Global existence
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Local and Global Existence of Solutions to Initial Value Problems of Nonlinear Kaup-Kupershmidt Equations 被引量:6
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作者 Shuang Ping TAO Shang Bin CUI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第4期881-892,共12页
This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt + α1 uδ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x,t)∈ E R^2, and δu/δt + α2 δu/δx ... This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt + α1 uδ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x,t)∈ E R^2, and δu/δt + α2 δu/δx δ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x, t) ∈R^2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup- Kupershmidt equations. The results show that a local solution exists if the initial function u0(x) ∈ H^s(R), and s ≥ 5/4 for the first equation and s≥301/108 for the second equation. 展开更多
关键词 Kaup-Kupershmidt equation initial value problem SOLUTION Local existence Global existence
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On the initial value problem and scattering of solutions for the generalized Davey-Stewartson systems 被引量:6
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作者 王保祥 郭柏灵 《Science China Mathematics》 SCIE 2001年第8期994-1002,共9页
We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove tha... We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove that the scattering operator carries a band in Hs into Hs. 展开更多
关键词 Davey-Stewartson systems initial value problem Scattering operators Hs-solutions
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Initial and Boundary Value Problems for Two-Dimensional Non-hydrostatic Boussi nesq Equations 被引量:4
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作者 沈春 孙梅娜 《Journal of Shanghai University(English Edition)》 CAS 2005年第2期114-119,共6页
Based on the theory of stratification, the well-posedness of the init ial and boundary value problems for the system of two-dimensional non-hydrosta ti c Boussinesq equations was discussed. The sufficient and necessa... Based on the theory of stratification, the well-posedness of the init ial and boundary value problems for the system of two-dimensional non-hydrosta ti c Boussinesq equations was discussed. The sufficient and necessary conditions of the existence and uniqueness for the solution of the equations were given for s ome representative initial and boundary value problems. Several special cases we re discussed. 展开更多
关键词 STRATIFICATION initial value problem boundary value problem well-posedness.
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INITIAL VALUE PROBLEMS AND FIRST BOUNDARY PROBLEMS FOR A CLASS OF QUASILINEAR WAVE EQUATIONS 被引量:5
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作者 陈国旺 杨志坚 赵占才 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1993年第4期289-301,共13页
The initial value problems and the first boundary problems for the quasilinear wave equation u_(tt)-[a_0+na_1(u_x)^(n-1)]u_(xx)-a_2u_(xxtt)=0 are considered,where a_0,a_2>0 are constants,a_1 is an arbitrary real nu... The initial value problems and the first boundary problems for the quasilinear wave equation u_(tt)-[a_0+na_1(u_x)^(n-1)]u_(xx)-a_2u_(xxtt)=0 are considered,where a_0,a_2>0 are constants,a_1 is an arbitrary real number,n is a natural number.The existence and uniqueness of the classical solutions for the initial value problems and the first boundary problems of the equation (1) are proved by the Galerkin method. 展开更多
关键词 Quasilinear wave equations initial value problems and first boundary problems Galerkin method.
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A Note on Initial Value Problem for the Generalized Tricomi Equation in a Mixed-type Domain 被引量:2
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作者 Kang Qun ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第8期1581-1596,共16页
In this paper, we study the well-posedness of initial value problem for n-dimensional gener-alized Tricomi equation in the mixed-type domain {(t,x):t∈[1,+∞),x∈Rn} with the initial data given on the line t=1 in... In this paper, we study the well-posedness of initial value problem for n-dimensional gener-alized Tricomi equation in the mixed-type domain {(t,x):t∈[1,+∞),x∈Rn} with the initial data given on the line t=1 in Hadamard's sense. By taking partial Fourier transformation, we obtain the explicit expression of the solution in terms of two integral operators and further establish the global estimate of such a solution for a class of initial data and source term. Finally, we establish the global solution in time direction for a semilinear problem used the estimate. 展开更多
关键词 Generalized Tricomi equation SEMILINEAR initial value problem mixed-type domain
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