陆云光

陆云光，男，1962年12月29日生，民族 汉, 籍贯, 江苏响水 1983年7月在山东大学数学系获理学学士学位 1986年元月在山东大学数学系获理学硕士学位 1989年2月在中科院系统科学所获理学博士学位 1989年2月至1990年11月在中科院数学物理所任助理研究员 1990年12月至1993年11月在中科院数学物理所任副研究员 1993年12月至1998年8月在中科院数学物理所任研究员 1992年5月至1992年8月在英国Reading大学访问 1992年9月至1993年2月在英国Newcastle大学访问 1993年3月至1993年5月在以色列Tel Aviv大学合作研究 1994年3月至1994年7月在美国Stanford大学作访问教授 1994年8月在德国Heidelberg大学作校方聘请的客座教授 1994年12月至1995年11月在德国Heidelberg大学作洪堡研究学者 1995年12月至1996年5月在德国Heidelberg大学作SFB研究基金的客座研究员 1996年9月至1998年8月在意大利国际高等研究中心(SISSA)访问 1998年9月至1999年12月在巴西里约热内卢联邦大学作客座教授 1997年元月起任中国《数学物理学报》中、英文版编委 2001年元月起任哥伦比亚《数学会学报》副主编 2003年元月起任哥伦比亚国家科技委专家组委员 现为中国科技大学数学系教授和哥伦比亚国立大学数学系教授 科研情况 主持过的项目有 1. 中科院百人计划项目《非线性双曲守恒律的研究》，200万元，独立主持人， 2001－2003, 已完成 2. 中科院院长特别基金《补偿列紧理论与松驰现象》，9万元，独立主持人， 1997-1999，已完成 3. 国家自然科学青年基金项目《某些非线性双曲守恒律整体解的研究》(批准 号：19201038), 1.4万元，独立主持人，1993-1995，已完成 4. 中科院留学择优支持基金《补偿列紧理论的应用》，2万元，独立主持人， 1993，已完成 5. 国家“八·五”攀登项目《非线性科学》子课题《非线性发展方程》，5万 元，参加人(主持人：丁夏畦院士)，1991-1995，已完成 6. 中科院重大项目《数理科学》，20万元，主要参加人(主持人，丁夏畦院士)， 1988-1990，已完成 奖励 1. 1994年获国家科委、科协、团中央授予的《首届全国杰出青年科技标兵》称号 2. 1994年成果《补偿列紧理论与某些拟线性双曲守恒方程组》获中科院自然 科学奖贰等奖，完成人：陆云光、林培雄、陈贵强 3. 1995年获中科院青年科学家奖贰等奖 4. 论文《带小粘性的非齐项弹性方程组的存在性及渐近性》(英文)获湖北省 第四届自然科学优秀学术论文壹等奖 主要邀请报告 (1). One hour invited talk on Fourth World Congress of Nonlinear Analysis, Orlando, Florida, June30-July 7, 2004. (2). One invited talk on Second Congress of Mathematicans of Latin America, Cancun, Mexico, June20-June 26, 2004. (3). One invited talk on Fifth AIMS international conference on Dynamical Systems and Differential Equations, Los Angeles, USA, June 16-June 19, 2004. (4). One hour talk on Second International Congress: Nonlinear Dynamic Analysis, Moscow, Russia, June 3-8, 2002. (5). 45 minutes invited talk on Third World Congress of Nonlinear Analysis, Sicily, Italy, July 19-26, 2000. (6). 45 minutes invited talk on Second World Congress of Nonlinear Analysis, Athens, Greece, July 10-17, 1996. (7). One hour invited talk on Fifth International Colloquium on Differential Equations, Plovdiv, Bulgaria, August 18-23, 1994. (8).在2000年哥伦比亚国家数学大会上应邀做一个1小时报告和一个45分钟报告 (9).在2002年拉丁美州第十三届数学会议上应邀做一个1小时报告 在国外访问任职期间，曾应邀在英国牛津大学，Reading大学，Newcastle大学，德国Stutgart大学，Aachen高工，Oberwohlfach数学中心，瑞士Zurich高工，瑞典皇家科学研究所（RIT），意大利国际理论物理中心，SISSA，L'Aquila大学，美国Stanford大学，芝加哥大学，柯朗研究所以及希腊，葡萄牙，挪威，巴西，智利，阿根廷等数十个大学、研究所作学术报告。 目前所从事的研究工作的内容 几乎所有的应用科学，物理、化学、生物、力学等中的自然现象都满足一定的规律(例如守恒律)。这些规律最终都可以用偏微分方程(组)来描述。对这些方程的了解是自然科学发展的关键。同时偏微分方程与数学的其它分支，例如分析，几何，拓扑有着紧密的联系。对偏微分方程的研究有非常强的应用背景和理论价值。目前正在开展以下两方面工作： 1. 非线性双曲守恒律弱解的存在性： 这是一个古老而又充满生机的研究课题。一直吸引着众多著名数学家的高度重视,从Riemann，Friedrichs，Lax到DiPerna，P.L.Lions。在自然现象被应用科学家验证并归纳为确定的方程组之后，方程组解的存在与否是一个检验其正确与否的关键。利用补偿列紧理论研究了非线性双曲型方程组中许多有物理背景的问题，于2003年在美国CRC出版了此研究领域中唯一专著。 2. 退化抛物型弱解的正则性研究: 在这研究方向上一个重要的公开问题是如何获得高维空间中Holder连续解的最优Holder估计。基于前辈数学家的工作，我们给出了一般方程解的定量Holder指数估计。 论著目录 # The book “Hyperboilc Conservation Laws and the Compensated Compactness Method” was published by Chapman & Hall/CRC Press, USA in September, 2002. [1]. Viscosity and Relaxation Approximations of Hyperbolic-Elliptic Mixed Type System, Y. Lu and C. Klingenberg, Proceedings of A.M.S. 132(2004), No. 5, 1305-1309. [2]. A Mixed Type System of Three Equations Modelling Reaction Flows, Y. Lu and C. Klingenberg, Proceedings of A.M.S., 131(2003), 11, 3511-3516. [3]. The Global Lipchitz-Continuous Solutions of Isentropic Gas Dynamics, C. Klingenberg, Y. Lu and L. Rendon, Applicable Analysis 82(2003), 1, 35-43. [4]. $L1$-singular limit for the relaxation and viscosity approximations C. Klingenberg, Y. Lu and H.J. Zhao, Electron. J. Diff. Eqns., Vol. 2003(2003), No。 23, pp. 1-11. [5]. Regularity of viscosity solutions of a degenerate parabolic equation, Y. Lu and L. Qian, Proceedings of A.M.S.,130(2002), 999-1004. [6]. H\"older Estimates of Solutions on a Degenerate Diffusion Equation, Proceedings of A.M.S., 130(2002), 1339-1343. [7]. Relaxation Limit for Hyperbolic Systems in Chromatography, Proceedings of A.M.S., 130(2002), 3579-3583. [8]. H\"older Estimates of Solutions on the Equation $u_{t}= \Delta G(u)$, Y. Lu, I. Mantilla and L. Rendon, Applicable Analysis, 81(2002), 333-339. [9]. Singular Limits of Stiff Relaxation and Dominant Diffusion for Nonlinear Systems, Y. Lu, J. Diff. Equs. 179(2002), No. 2, 687-713. [10]. Relaxation Approximations and BV Estimates for Some Partial Differential Equations, F. Caicedo, Y. Lu and M. Sepulveda, Electron. J. Diff. Equs., Vol. 2002(2002), No. 19, pp. 1-10. [11]. On Solutions to Nonlinear Reaction-Diffusion-Convection Equations with Degenerate Diffusion, Y.Lu & W. Jaeger, J. Diff. Equas., 170(2001), No. 1, 1-21. [12]. Artificial and Physical Viscosity Solutions for a Hyperbolic Conservation System, Y. Lu and Mauricio Sepulveda, Applicable Analysis, 78(2001), 33-42. [13]. Convergence of Approximated Solutions to Nonstrictly Hyperbolic System, Y. Lu, I. Mantilla and L. Rendon, Advanced Nonlinear Studies, 1(2001), 65-79. [14].The relaxation limits for systems of Broadwell type, Y. Lu & C. Klingenberg, Differential and Integral Equations, Vol. 14(2001), No.1, 117-127. [15].Holder Estimates of Solutions of Biological Population Equations, Appl. Math. Letters, 13(2000), 123-126. [16].Holder Estimates of Solutions of Some Doubly Nonlinear Degenerate Parabolic Equations, Communcation in P.D.E., 24(1999), 5&6, 895-914. [17].The rate of convergence of the viscosity method for a nonlinear hyperbolic system, Y. G. Lu, P. K. Sweby and K. Chen, Nonlinear Analysis, 38(1999), 4: 435-445. [18].The vacuum case in Diperna's paper, C. Klingenberg and Y. Lu, J. Math. Anal. Appl. 1225(1998),679-684. [19].Existence of global solutions for viscoelastic systems, J. Math. Anal. Appl.. 218(1998), 175-182. [20].Existence of solutions to hyperbolic conservation laws with a source, Y. Lu & C. Klingenberg, Commun. Math. Phys., 187(1997),327-340. [21].Global regularity of solutions for general degenerate parabolic equations in 1-D, W Jaeger & Y. Lu, J. Diff. Equs., 140(1997), 365-377. [22].Convergence of the viscosity method for a nonstrictly hyperbolic system,Y.Lu, Z.Wang, C.Zhu and H.Zhao, J. Sys. Sci. & Math. Scis., 16(1996), 1: 36-47. [23].Existence of generalized solutions for some coupled systems of nonlinear hyperbolic equations, J. Sys. Sci. & Math. Scis., 16(1996),4: 125-135. [24].Riemann problem on some hyperbolic PDEs (in Chinese), Y. Lu and Benjing Xuan, Acta Math. Sci., 16(1996), 187-194. [25].Cauchy problem for hyperbolic conservation laws with relaxation term, C. Klingenberg & Y.Lu, Proc. Roy. Soc. Edin. 126(1996), 821-828. [26].The Cauchy problem for hyperbolic conservation laws with three equations, Y.Lu & C. Klingenberg, J. Math. Appl. Anal., 202(1996), 206-216. [27].The Cauchy problem for reaction-convection equations in higher-dimensional spaces, Acta Math. Sci., 14(1994), 3:332-336. [28].Convergence of the viscosity method for some nonlinear hyperbolic systems, Proc. Roy. Soc. Edin. 124A(1994), 341-352 [29].Cauchy problem for a hyperbolic model, Nonlinear Analysis, TMA, 23(1994), 9: 1135-1144 [30].Global Holder Continuous Solutions of Nonstrictly Hyperbolic Systems, J. Partial Diff. Equs., 7(1994),132-142 [31].Global Holder Continuous Solution of Isentropic Gas Dynamics, Proc. Roy. Soc. Edin. 123A(1993), 231-238 [32].Viscous solutions of quadratic conservation laws with umbilic points, Y. Lu, C.Zhu & H. Zhao, Nonlinear Analysis, TMA. 21(1993), 7, 485-499 [33].Global classical solution of the Cauchy problem for two-dimensional gas dynamics system, Acta Math. Sci., 13(1993),1: 65-73 [34].Existence of generalized solutions to a hyperbolic model of combustion, Y.Lu & Jiaxin Hu, Acta Math. Sci., 13(1993), 2:195-201 [35].Existence and asymptotic behavior of solutions to inhomogeneous 2 by 2 hyperbolic quadratic conservation laws with small viscosity, Y.Lu & C.Zhu, J. Sys. Sci. & Math.Scis. 13(1993), 297-304 [36].Convergence of the viscosity method for a nonstrictly hyperbolic conservation laws, Comm. in Math. Phys., 150(1992), 59-64 [37].Cauchy problem for an extended model of combustion, Proc. Roy. Soc. Edin. 120A(1992), 349-360 [38].The interactions of elementary waves of nonstrictly hyperbolic system, Y. Lu & Jinghua Wang, J. Math. Anal. Appl., 166(1992),1:136-169 [39].Convergence of the viscosity method for a nonstrictly hyperbolic system, Acta Math. Sci., 12(1992), 2: 230-239 [40].Existence and asymptotic behavior of solutions to inhomogeneous systems of gas dynamics with viscosity, Acta Math. Sci., 12(1992), 1:51-61 [41].Existence and asymptotic behavior of solutions to inhomogeneous equations of elasticity with little viscosity, Nonlinear Analysis, TMA. 16(1991) 3:197-207 [42].Existence and asymptotic behavior of solutions to 2 by 2 hyperbolic quadratic conservation laws with viscosity, Y.Lu & H.Zhao, Nonlinear Analysis, TMA. 17(1991), 2:169-180 [43].Convergence of the approximation solutions to isentropic gas dynamics, Guiqiang Chen & Yunguang Lu, Acta Math. Sci., 10(1990), 1:39-46 [44].Existence and asymptotic behavior of solutions to gas dynamics systems with diferent viscosity coefficients, Chin. Sci. Bull., 35(1990), 9:785-786 [45].The study on application way of the compensated compactness theory, Guiqiang Chen & Yunguang Lu, Chin. Sci. Bull., 34(1989),1:15-19 [46].Convergence of solutions to nonlinear dispersive equations without convexity conditions, Applicable Analysis, 31(1989),4:239-246 [47].Asymptotic behavior of solutions of initial problem to systems of gas dynamics with viscous term, Chin. Sci. Bull., 34(1989),1: 7-11 [48].Existence of solutions for inhomogeneous systems of gas dynamics, Guiqiang Chen & Y.Lu, Acta Math. Sci., 9(1989), 2: 121-130 [49].A study of approaches to applying the theory of compensated compactness, Guiqiang Chen and Y. Lu, Kexue-Tongbao (Chinese) [Chinese-Academy-of-Science.- Kexue-Tongbao (Science Bulletin)] 33 (1988), no. 9, 641--644. [50].Asymptotic behavior of solutions to the gas dynamics equations with a viscosity term, Yunguang Lu, Kexue-Tongbao (Chinese) [Chinese-Academy-of-Science.- Kexue-Tongbao (Science Bulletin)] 33 (1988), no. 1, 4--7. [51].The asymptotic behavior of solutions of initial value problem to system of gas dynamics with viscosity, Y. Lu & Guiliang Xie, Acta Math. Sci., 8(1988),2: 185-198 [52].Existence and asymptotic behavior of solutions to systems of gas dynamics with a class of sources, Guiqiang Chen & Y.Lu, Acta Math.Sci., 8(1988),1:85-94 [53].Existence and asymptotic behavior of global solutions of the Cauchy problem for inhomogeneous systems of isentropic gas motion with viscosity, G. Wang, G. Xie and Y. Lu, J. Cent. China Norm. Univ., Nat. Sci. 22, No.2, 129-134 (1988). [54].On the antiblowing-up and antiquenching problems for semilinear parabolic equations, J. Sun and Y. Lu, J. Shandong Univ., Nat. Sci.,22, No.2, 26-34 (1987). [55]. Convergence of Viscosity Solutions to a Nonstrictly Hyperbolic System, in the book "Advances in Nonlinear Differential Equations and Related Areas", World Scientific(1998), PP. 250-266. [56]. A study of the global weak solution for the isentropic equations of polytropic gas, A.Jeffrey & Y. Lu, AMS/IP Studies in Advanced Mathematics, Volume 3, 1997(261-270). [57]. Existence of solutions to resonant systems of conservationlaws, C. Klingenberg & Y. Lu, Collection: Hyperbolic problems: theory, numerics, applications (Stony Brook, NY,1994),383--389 World Sci. Publishing, River Edge, NJ, 1996. [58]. Cauchy problem for hyperbolic conservation laws with relaxation terms, C. Klingenberg & Y. Lu, Matematica Contemporanea, Vol.11, 1996(51-60).