检索结果-南通市图书馆

Global Existence and Blow up for Damped Generalized Boussinesq Equation

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2017年第1期33卷 251-262页

作者： Run-zhang XU Yong-bing LUO Ji-hong SHEN Shao-bin HUANG College of Science Harbin Engineering University Harbin 150001 China College of Automation Harbin Engineering University Harbin 150001 China College of Computer Science and Technology Harbin Engineering University Harbin 150001 China

We study the cauchy problem of damped generalized Boussinesq equation utt - uxx ＋（uxx＋ f（u））xx - αuxxt = 0. First we give the local existence of weak solution and smooth solution. Then by using potential well method and convexity method we prove the global existence and finite time blow up of solution, then we obtain some sharp conditions for the well-posedness problem.

关键词： generalized Boussinesq equation damping cauchy problem global existence blow up

Global Existence and Pointwise Estimates of Solutions to Generalized Benjamin-Bona-Mahony Equations in Multi Dimensions

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2014年第4期35卷 659-668页

作者： Hongmei XU Yan LIANG College of Science Hohai University

This paper is concerned with the global existence and pointwise estimates of solutions to the generalized Benjamin-Bona-Mahony equations in all space *** using the energy method, Fourier analysis and pseudo-differential operators, the global existence and pointwise convergence rates of the solution are obtained. The decay rate is the same as that of the heat equation and one can see that the solution propagates along the characteristic line.

关键词： cauchy problem Generalized Benjamin-Bona-Mahony equations Multidimensions Global existence Pointwise estimates

一类半线性波动方程具分块常数初值的cauchy问题

在线全文

学校读者我要写书评

暂无评论

Northeastern Mathematical Journal 1994年第3期10卷 421-426页

作者：张永前

In this Paper,we study the existence and regularity of the weak solution to with piecewise constants data near the origin. We also give a generalization to the semilinear SyStems.

关键词： cauchy problem Piecewise Constants Data Semilinear Wave Equation Weak Solution Singularity

Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2011年第5期32卷 771-780页

作者： Yi ZHOU 11 Key Laboratory of Mathematics for Nonlinear Sciences,Ministry of Education,China Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences,Fudan University,Shanghai 200433,China. Key Laboratory of Mathematics for Nonlinear Sciences Ministry of Education China Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai China

The author considers the cauchy problem for quasilinear inhomogeneous hyperbolic *** the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in *** ***.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.

关键词： cauchy problem Global classical solution Partially dissipativequasilinear hyperbolic system

Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2 1 Nonlinear Mathematical Modeling and Methods Laboratory Shanghai Key Laboratory for Contem- porary Applied Mathematics School of Mathematical Sciences, Fudan University, Shanghai 200433, China. 2 School of Mathematical Sciences, Fudan University, Shanghai 200433, China Department of Mathematics, North University of China, Taiyuan 030051, China. Nonlinear Mathematical Modeling and Methods Laboratory Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai China School of Mathematical Sciences Fudan University Shanghai China Department of Mathematics North University of China Taiyuan China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation cauchy problem Lifespan

Solution to Nonlinear Parabolic Equations Related to P-Laplacian

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2012年第5期33卷 767-782页

作者： Huashui ZHAN School of Sciences Jimei University Xiamen 361021 Fujian China. E-mail: hszhan@***

Consider the following cauchy problem：where 1 〈 p 〈 2, 1 〈 m 〈 p_~11, and # is a a-finite measure in N. By the Moser＇s iteration method, the existence of the weak solution is obtained, provided that （M＋1）N 〈 P. In mN＋l contrast, if 〉 p, there is no solution to the cauchy problem with an initial value δ（X）, where 5（x） is the classical Dirac function.

关键词： Nonlinear parabolic equation cauchy problem Existence a-Finite measure

A hybrid method for inverse cavity scattering problem for shape

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2010年第2期25卷 127-136页

作者： LIU Juan MA Fu-ming School of Mathematics, Jilin University, Changchun 130012, China. School of Mathematics Jilin University Changchun China

In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.

关键词： Open cavity cauchy problem Helmholtz equation integral equations system method iterativehybrid method.

Formation of Singularities in One—Dimensional Hydromagnetic Flow

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2002年第4期37卷 385-392页

作者： KONGDe－Xing DepartmentofAppliedMathematics ShanghaiJiaoTongUniversityShanghai200030China

Two results on the formation of singularities in solutions to the system of one-dimensional hydromagnetic dynamics are *** particular,it is shown that shocks form from a smooth spatial periodic flow in a finite time if the initial amounts of entropy and the “magnetic field” in each period are smaller than those of sound waves.A quantitative estimate of blow-up time is also given.

关键词： system of hydromagnetic dynamics cauchy problem periodic flow blow-up

ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2002年第3期23卷 317-324页

作者： J.P.DIAS M.FIGUEIRA Dedicated to the memory of Jacques-Louis Lions Dedicated to the memory of Jacques-Louis Lions

This paper is a continuation of the authors' previous paper [1]. In this paper the authors prove, assuming additional conditions on the initial data, some results about the existence and uniqueness of the entropy weak... 详细信息

关键词： cauchy problem Weak solution Quasilinear hyperbolic system