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SOME RESULTS ON A DEGENERATE AND SINGULAR DIFFUSION EQUATION

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Acta Mathematica Scientia 2007年第3期27卷 581-601页

作者：姚正安周文书 department of mathematics Zhongshan University

In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also... 详细信息

关键词： Degenerate and singular diffusion equation weak solution existence asymptotic behavior

Effective stability for generalized Hamiltonian systems

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Science china mathematics 2004年第5期47卷 675-686页

作者： CONG Fuzhong & LI YongSchool of mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, china Office of mathematics, changchun Flight Academy of the Air Force, changchun 130022, china department of mathematics, jilin university, changchun 130012, china 1. School of mathematics and Information Science Shandong Institute of Business and Technology 264005 Yantai China 2. Office of mathematics Changchun Flight Academy of the Air Force 130022 Changchun China 3. department of mathematics Jilin University 130012 Changchun China

An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems,dimensions of action variables and angle variables ... 详细信息

关键词： Effective stability, generalized Hamiltonian systems, Lochak's technique.

LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES

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Acta Mathematica Scientia 2010年第3期30卷 968-974页

作者：王路生尹景学王泽佳 department of mathematics Jilin University department of mathematics South China Normal University

This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations ｜x｜λ＋Эt^-Эu=div（｜x｜^k∨u^m）＋｜x｜λ＋ku^p with 0 〈 m 〈 1,p 〉 1,λ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and kl for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k E （k∞, k1）, otherwise, pc is infinite or does not exist.

关键词： Newtonian filtration equation critical exponent exterior problem Thresh -old

Some properties of Young measure solutions for a class of nonlinear diffusion equations

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Progress in Natural Science:Materials International 2002年第7期 34-39页

作者： WANG Chunpeng and YIN Jingxue(department of mathematics, jilin university, changchun 130012, china) department of mathematics Jilin University Changchun 130012 China

This paper is concerned with the first initial-boundary value problem of a class of singular diffusion equations with the flux sublinear growth and the potential without convexity, in which the properties of Young measure solutions are discussed, and the uniqueness, stability are proved, and the asymptotic behaviors of solutions and their energy as the time goes to infinity are investigated.

关键词： singular diffusion equations forward-backward Young measure solutions.

Existence of Young measure solutions of a class of singular diffusion equations

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Progress in Natural Science:Materials International 2002年第4期 20-25页

作者： YIN Jingxue and WANG Chunpeng(department of mathematics, jilin university, changchun 130012, china) department of mathematics Jilin University Changchun 130012 China

The first initial-boundary value problem of a class of singular diffusion equations with the flux sublinear growth and the potential without convexity is investigated. Such equations may be strongly degenerate, singular and forward-backward. Inspired by the idea in a recent work of Demoulini, we first discuss the regular case by introducing the Young measure solutions and prove the existence of such solutions. Consequently, we approximate the extreme case by the method of regularization. By means of some uniform estimates and some techniques, the existence of Young measure solutions with bounded variation is established.

关键词： singular diffusion equations forward-backward Young measure solutions.

Arnold's theorem on properly degenerate systems with the Russmann nondegeneracy

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Science china mathematics 2005年第12期48卷 1656-1669页

作者： HAN Yuecai & LI Yong College of mathematics, jilin university, changchun 130012, china 1. College of mathematics Jilin University 130012 Changchun China

In this paper, we investigate the persistence of invariant tori for the nearly in-tegrable Hamiltonian system H(x,y) = h(y) + εp(x,y) + ε2Q(x,y), where h(y) and εp(x,y) satisfy the Russmann non-degenerate condition. Mainly we overcome the difficulties that the order of the parameter E in the perturbation ε2Q(x,y) is not enough and that the measure estimate involves in parts of frequencies with small parameter.

关键词： Arnold’s theorem the Russmann non-degenerate condition.

NUMERICAL COMPUTATION OF BOUNDED SOLUTIONS FORA SEMILINEAR ELLIPTIC EQUATION ON AN INFINITE STRIP

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Journal of Computational mathematics 1999年第2期17卷 159-170页

作者： Fu-ming Ma(department of mathematics, jilin ’university, changchun 130023, china) 吉林大学数学系吉林长春

In this paper, we consider the computation of bounded solutions of a semilinear elliptic equation on an infinite strip. The dynamical system approach and reduction on center manifold are used to overcome the difficult... 详细信息

关键词： numerical method nonlinear PDE center manifold

Kernel model-based diagnosis

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Progress in Natural Science:Materials International 2002年第2期12卷 63-67页

作者： OUYANG Dantong(department of Computer Science, jilin university, changchun 130012, china) jilin Univ Dept Comp Sci Changchun 130012 Peoples R China

The methods for computing the kernel consistency-based diagnoses and the kernel abductive diagnoses are only suited for the situation where part of the fault behavioral modes of the components are known. The characterization of the kernel model-based diagnosis based on the general causal theory is proposed, which can break through the limitation of the above methods when all behavioral modes of each component are known. Using this method, when observation subsets deduced logically are respectively assigned to the empty or the whole observation set, the kernel consistency-based diagnoses and the kernel abductive diagnoses can deal with all situations. The direct relationship between this diagnostic procedure and the prime implicants/implicates is proved, thus linking theoretical result with implementation.

关键词： model-based diagnosis general causal theory prime implicant/implicate diagnostic space.

A hybrid method for inverse cavity scattering problem for shape

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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.