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| 1 | LIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATALIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATA显示文摘The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with 'slow' decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data. | KONG DEXING (Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030, China.) | 2000 | Chinese Annals of Mathematics,Series B2000，21，4： | 14 |
| 2 | MODELLING AND STABILITY ANALYSIS OF POPULATION GROWTH WITH SPATIAL DIFFUSION显示文摘In recent years, population growth models with spatial diffusion have beenextensively studied by many authors (for example, see [1-5]). In this paper, a populationgrowth model is considered with a discrete age-dependence and spatial diffusion, and isinvestigated in a semigroup framework. The spectral properties of the population oper-ator are given. On the basis of such spectral consideration, the asymptotic behaviourof the semigroup generated by the population operator is obtained. Finally, a nonlinearpopulation growth model is considered and its stability is analyzed. | W.L.CHAN FENG Dexing Department of Mathematice,the Chinese University of Hong Kong,Shatin,N.T,Hong Kong Institute oj Systems Science, Academia Sinica, Beijing 100080, China | 1993 | Systems Science and Mathematical Sciences1993，6，4： | 10 |
| 3 | Symmetry Reduction and Exact Solutions of a Hyperbolic Monge-Ampère Equation显示文摘By means of the classical symmetry method,a hyperbolic Monge-Ampère equation is investigated.The symmetry group is studied and its corresponding group invariant solutions are constructed.Based on the associated vector of the obtained symmetry,the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampère equation,from which two interesting classes of solutions to the hyperbolic Monge-Ampère equation are obtained successfully. | Zhongzhou DONG Yong CHEN Dexing KONG Zenggui WANG | 2012 | Chinese Annals of Mathematics,Series B2012，33，2： | 4 |
| 4 | Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases显示文摘In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases. | KONG DeXing 1 , LIU KeFeng 2 & WANG YuZhu 3, 1 Department of Mathematics, Zhejiang University, Hangzhou 310027, China 2 Department of Mathematics, University of California at Los Angeles, CA 90095, USA 3 Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200248, China | 2010 | Science China Mathematics2010，53，3： | 4 |
| 5 | Time-periodic solutions of the Einstein's field equations Ⅲ:physical singularities显示文摘In this paper we construct a new time-periodic solution of the vacuum Einstein's field equations, this solution possesses physical singularities, i.e., the norm of the solution's Riemann curvature tensor takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the 'time-periodic physical singularity'. By calculating the Weyl scalars of this solution, we investigate new physical phenomena and analyze new singularities for this universal model. | KONG DeXing LIU KeFeng SHEN Ming | 2011 | Science China Mathematics2011，54，1： | 2 |
| 6 | Cauchy problem for quasilinear hyperbolic systems 显示文摘 | Kong Dexing | 2000 | Mathematical Society of Japan2000，6，： | 1 |
| 7 | Blow up of periodic solutions to quasilinear hyperbolic systems显示文摘 | | 1996 | Nonlinear Analysis:Theory Methods and Applications1996，26，： | 1 |
| 8 | Global classical solutions to quasilinear hyperbolic systems with decay initial data显示文摘 | Kong Dexing and Zhou Yi | 1997 | Nonlinear Analysis Theory Methods & Applications1997，28，： | 1 |
| 9 | Wave character of metrics and hyperbolic geometric flow显示文摘 | Kong Dexing Liu Kefeng | 2007 | J Math Phys2007，48，： | 1 |
| 10 | Geometric approach for finding exact solutios to nonlinear partial differential equations显示文摘 | Kong Dexing Hu Hairong | 1998 | Physics Letters A1998，246，： | 1 |
| 11 | New explicit exact solitary wave solutions for a new Hamiltonlan amplitude equation显示文摘 | Kong Dexing Zhang Weiguo | 1994 | Physics Letters A1994，190，： | 1 |
| 12 | Exact solutions to a class of quasilinear hyperbolic systems显示文摘 | Kong Dexing Ni Guangjlong | 1995 | Physics Letters A1995，204，： | 1 |
| 13 | An Improved LOT Model for Image Restoration显示文摘 | Fangfang Dong Zhen Liu Dexing Kong Kefeng Liu | 2009 | Journal of Mathematical Imaging and Vision2009，，1： | 1 |
| 14 | Geometric approach for finding exact solutios to nonlinear partial differential equations显示文摘 | Kong Dexing Hu Hairong | 1998 | Physics Letters A1998，246，： | 1 |
| 15 | New explicit exact solitary wave solutions for a new Hamiltonian amplitude equation显示文摘 | Kong Dexing Zhang Weiguo | 1994 | Physics Letters A1994，190，： | 1 |
| 16 | Explicit exact solutions for the Lienard equation and its applications显示文摘 | Kong Dexing | 1995 | Physics Letters A1995，196，： | 1 |
| 17 | Exact solutions to a class of quasilinear hyperbolic systems显示文摘 | Kong Dexing Ni Guangjiong | 1995 | Physics Letters A1995，204，： | 1 |
| 18 | Global classicalsolutions to quasilinear hyperbolic systems with decay ini-tial data 显示文摘 | Kong Dexing and Zhou Yi | 1997 | Nonlinear Analysis Theory Methods &Applications1997，28，： | 1 |
| 19 | Global classicalsolutions for non- strictly quasilinear hyperbolic systems显示文摘 | Kong Dexing and Zhou Yi | 1996 | Nonlinear Studies1996，3，： | 1 |
| 20 | Dissipative hyperbolic geometric flow显示文摘 | Dai Wenrong Kong Dexing Liu Kefeng | 2008 | Asian J Math2008，12，： | 1 |
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