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On the initial value problem and scattering of solutions for the generalized Davey-Stewartson systems

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Science China Mathematics 2001年第8期44卷 994-1002页

作者：王保祥郭柏灵 Department of Mathematics Hebei University Baoding China Institute of Applied Physics and Computational Mathematics Beijing China

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... 详细信息

关键词： Davey-Stewartson systems initial value problem Scattering operators Hs-solutions

A Note on initial value problem for the Generalized Tricomi Equation in a Mixed-type Domain

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Acta Mathematica Sinica,English Series 2013年第8期29卷 1581-1596页

作者： Kang Qun ZHANG Department of Mathematics and Physics Nanjing Institute of Technology

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.

关键词： Generalized Tricomi equation semilinear initial value problem mixed-type domain

THE STABILITY ON THE SOLUTION OF THE initial value problem

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Applied Mathematics and Mechanics(English Edition) 1991年第10期12卷 1001-1008页

作者：邵孝湟 Hangzhou Normal College Hangzhou

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 n... 详细信息

关键词： stability initial value problem differentiability

A second-order finite difference scheme for singularly perturbed initial value problem on layer-adapted meshes

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第3期10卷 123-145页

作者： S.R.Sahu J.Mohapatra Department of Mathematics National Institute of Technology Rourkela India

In this paper,a second-order singularly perturbed initial value problem is considered.A hybrid scheme which is a combination of a cubic spline and a modified midpoint upwind scheme is proposed on various types of layer-adapted *** error bounds are established for the numerical solution and for the scaled numerical derivative in the discrete maximum *** is observed that the numerical solution and the scaled numerical derivative are of second-order convergence on the layer-adapted meshes irrespective of the perturbation *** show the performance of the proposed method,it is applied on few test examples which are in agreement with the theoretical ***,existing results are also compared to show the robustness of the proposed scheme.

关键词： Singular perturbation initial value problem hybrid scheme layer-adapted mesh uniform convergence

initial value problem of Singular n-Laplacian Equation

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Journal of Beijing Institute of Technology 2001年第3期10卷 225-232页

作者：王宏洲葛渭高北京理工大学应用数学系北京100081

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... 详细信息

关键词： initial value problem n Laplacian operator positive solution cone

initial value problemS FOR SECOND ORDER IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

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Chinese Annals of Mathematics,Series B 1997年第4期18卷 439-448页

作者： GUO DAJUN Department of Mathematics Shandong UniverstyJinan 250100ShandongChina

This paper investigates the maximal and minimal solutions of initial value problem for second order nonlinear impulsive integro differential quation in a Banach space by establishing a comparison result and using the ... 详细信息

关键词： Impulsive integro differential equation Banach space initial value problem Comparison result

initial value problems for Second Order Impulsive Integro-Differential Equation in Banach Spaces

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Transactions of Tianjin University 2005年第1期11卷 73-78页

作者：陈芳启张海燕 Department of Mathematics School of Sciences Tianjin University Tianjin 300072 China

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 *** the same time, another sufficient condition of existence of minimal and maximal solutions based on the Kuratowski measure of noncompactness is given.

关键词： impulsive integro-differential equation initial value problem comparison result

Local and Global Existence of Solutions to initial value problems of Nonlinear Kaup-Kupershmidt Equations

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Acta Mathematica Sinica,English Series 2005年第4期21卷 881-892页

作者： Shuang Ping TAO Shang Bin CUI Department of Mathematics. Northwest Normal University Lanzhou 730070 P. R. China Department of Mathematics Zhongshan University Guangzhou 510275 P. R. China

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.

关键词： Kaup-Kupershmidt equation initial value problem Solution Local existence Global existence

Local and Global Existence of Solutions to initial value problems of Modified Nonlinear Kawahara Equations

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Acta Mathematica Sinica,English Series 2005年第5期21卷 1035-1044页

作者： Shuang Ping TAO Shang Bin CUI Department of Mathematics Northwest Normal University Lanzhou 730070 P. R. China Department of Mathematics Zhongshan University Guangzhou 510275 P. R. China

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^*** 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.

关键词： Kawahara equation initial value problem Solution Local existence Global existence