姓名：陆云光

职称：教授

办公室：闻理园A4-304-1

邮箱：ylu2005@ustc.edu.cn

研究方向：非线性偏微分方程

个人简介：

    陆云光，二级教授、博士生导师，哥伦比亚国家科学院院士，享受国务院政府特殊津贴，曾为德国洪堡基金获得者, 中国科学院“百人计划”特聘教授、浙江省特聘专家、浙江省高校钱江学者特聘教授，被国家科委、科协、团中央授予首届全国青年科技标兵称号, 获江苏省五一劳动荣誉奖章，曾获全国百篇优秀博士学位论文提名导师奖、中国科学院优秀博士学位论文导师奖。作为第一完成人获得中科院自然科学奖二等奖、中科院青年科学家奖二等奖、湖北省自然科学优秀学术论文一等奖、安徽省第五届自然科学优秀学术论文一等奖、浙江省自然科学奖三等奖、浙江省自然科学学术奖一等奖、浙江省高校科研成果奖二等奖等。在Arch. Rat. Mech. Anal.、Commun. Math. Phys.、Math. Ann.、JFA、SIAM J. Math. Anal.、CPDE、Israel J. Math.等学术杂志发表100余篇学术论文，在美国CRC出版社和中国科学出版社各出版专著一本。

 

学术研究：

学术著作

1. Yunguang Lu, “Hyperboilc Conservation Laws and the Compensated Compactness Method” Chapman & Hall/CRC Press,128, USA, 2003.

2. 陆云光 和 陈志新，补偿列紧方法和双曲守恒律, 科学出版社, 2011年.

 

学术论文

[101] Y. Lu, Global solutions and relaxation limit to the Cauchy problem of a hydrodynamic model for semiconductors, J. Differential Equations, 393 (2024) 343-368.

[100] X. Wang, Y. Lu and C. Klingenberg, Viscosity-flux approximation method to inhomogeneous system of isentropic gas dynamics, J. Math. Anal. Appl. 531 (2024) 127872.

[99] Y. Lu, J. Chen, W. Jiang, C. Klingenberg and G. You, The global existence of L∞ solutions to isentropic Euler equations in general nozzle, Math Nachr. 297 (2024) 38-51.

[98] Y. Chen, C. Klingenberg, Y. Lu, X. Wang and G. You, Invariant region on a non-isentropic gas dynamics system, Nonlinear Analysis, Real World Applications 73 (2023) 103915.

[97] X. Wang, Y. Lu, R. de la Cruz and G. You, Global solutions to a hydrodynamic model for semiconductors with velocity relaxation, Acta Math. Sci. 43 (2023) 975-980.

[96] X. Jia, C. Klingenberg, Y. Lu and Q. Sun, Existence of entropy solutions to system of polytropic gas with a class of unbounded sources, Journal of Nonlinear and Variational Analysis, 7 (2023) 437-448.

[95]X. Wang, Y. Lu, Q. Sun and C. Xue, Solutions for a nonstrictly hyperbolic and genuinely nonlinear system, Journal of Nonlinear and Variational Analysis, 7 (2023) 201-207.

[94] S. Yin, X. Wang, Y. Lu and C. Klingenberg, Global solutions of the Cauchy problem to Euler-Poisson equations of two-carrier types, Appl. Math. Let. 132 (2022) 108174.

[93]. Y. Hu, C. Klingenberg and Y. Lu, Zero Relaxation time limits to a hydrodynamic model of two carrier types for semiconductors, Mathematische Annalen, (2022) 382:1031-1046

[92]. C. Xue, C. Klingenberg, Y. Lu and J. Zhang, Zero relaxation time limits to isothermal hydrodynamic model for semiconductor, Appl. Math. Letters, 109(2020), 106528.

[91]. Y. Lu, Existence of global solutions for isentropic gas flow with friction, Nonlinearity, 33(2020), 3940-3969.

[90]. Y. Hu, Y. Lu and N. Tsuge, Global existence and stability to the polytropic gas dynamics with an outer force, Appl. Math. Letters, 95(2019), 35-40.

[89] Q. Sun, Y. Lu and C. Klingenberg, Global solutions to system of isentropic gas dynamics in a divergent nozzle with friction,  Acta Matematica Scientia, 39B(2019), 1213-1218..

[88]. Y. Lu, Global solutions to isothermal system in a divergent nozzle with friction, Appl. Math. Letters, 84(2018), 176-180.

[87]. Y. Lu and Y. Sugiyama, Existence and nonexistence theorems of global weak solutions to degenerate quasilinear wave equations for the elasticity, Appl. Math. Letters, 84(2018), 118-123.

[86]. Y. Lu, Global weak solutions for the chromatography system, Israel Journal of Mathematics, 225(2018), No. 2, 721-741.

[85]. Y. Lu, Global existence of solutions to system of polytropic gas dynamics with friction, Nonlinear Analysis, Real World Applications, Volume 39, 2018, 418-423.

[84]. Y. Lu, V. Elder and J. Xie, Global existence of weak solutions for n×n system of chromatography, Nonlinear Analysis, Real World Applications, Volume 37, 2017, 309-316

[83]. Y. Lu, Global Entropy Solutions of Cauchy Problem for the Le Roux System, Applied Mathematics Letters, 60(2016), 61-66.

[82]. Y. Lu, X. Lu and C. Klingenberg, The Cauchy problem for multiphase first-contact miscible models with viscous fingering,  Nonlinear Analysis, Real World Applications, 27(2016), 43-54.

[81]. Y. Lu, C. Klingenberg, U. Koley and X.Z. Lu, Decay rate for degenerate convection diffusion equations in both one and several space dimensions, Acta Matematica Scientia, 35B(2015), 281-302.

[80]. Y. Lu, C. Klingenberg, L. Rendon and D. Zheng, Global Solutions for a Simplified Shallow Elastic Fluids Model, Abstract and Applied Analysis, Vol. 2014, Article ID 920248, 5 pages.

[79]. J. Caicedo, C. Klingenberg, Y. Lu and L. Rendon, Hyperbolic approximation on system of elasticity in Lagrangian coordinates, Natural Sciences, 6 (2014), 477-486.

[78]. D. Zheng, Y. Lu, G. Song, and X. Lu, Global existence of solutions for a nonstrictly hyperbolic system, Abstract and Applied Analysis, Vol. 2014, Article ID 691429, 7 pages.

[77]. Y. Lu, I. Mantilla, L. Rendon and D. Zheng, A new application of the flux approximation method on hyperbolic conservation systems,  Advances in Pure Mathematics, 2013, 3, 698-702.  

[76]. Y. Lu, Existence of global weak entropy solutions to some nonstrictly hyperbolic systems, SIAM. Journal on Math. Anal., Vol. 45(2013), No. 6, pp. 3592–3610.

[75]. Y. Lu, Existence of global entropy solutions to general system of Keyfitz-Kranzer type, J. Funcl. Anal., 264 (2013), 2457-2468 .

[74]. F. Gu, Y. Lu and Q. Zhang, Global solutions to one-dimensional shallow water magnetohydrodynamic equations, J. Math. Anal. Appl., 401 (2013), 714-723.

[73]. Y. Lu and F. Gu, Existence of global entropy solutions to the isentropic Euler equations with geometric effects, Nonlinear Analysis, Real World Applications, 14(2013), 990-996.

[72]. Y. Lu and F. Gu, Existence of global bounded weak solutions to Keyfitz-Kranzer system, Commun. Math. Sci., 10 (2012), No.4, 1133-1142.

[71]. Y. Lu, Existence of global bounded weak solutions to a symmetric system of Keyfitz-Kranzer type, Nonlinear Analysis, Real World Applications, 13(2012),235-240.

[70].Y. Lu, Existence of global bounded weak solutions to a non-symmetric system of Keyfitz-Kranzer type, J. Funct. Anal., 261(2011), 2797-2815.

[69]. Y. Lu, Global existence of solutions to resonant system of isentropic gas dynamics, Nonlinear Analysis, Real World Applications, 12(2011),2802-2810.

[68]. Y. Lu, Resonance for the isothermal system of isentropic gas dynamics, Proc. A.M.S., 139 (2011) 2821-2826.

[67]. Y. Lu, Y. Peng and C. Klingenberg, Existence of global solutions to isentropic gas dynamics equations with a source term, Science China, 53 (2010), 1: 115-124.

[66]. Y. Lu and C. Klingenberg, Singular Limits for Inhomogeneous Equations of Elasticity, Acta Math. Sci., 29B(2009), No. 3, 645-649(吴文俊院士九十大寿专缉).

[65]. Y. Lu, Strong entropy for system of isentropic gas dynamics, Acta Math. Appl. Sinica, Vol. 24, 3(2008), 405-408(丁夏畦院士八十大寿专缉).

[64]. Y. Lu, Nonlinearly degenerate wave equation, Rev. Acad. Colomb. Cienc. Vol. XXXI, No. 119(2007), 275-283

[63]. Y. Lu, Some results on general system of isentropic gas dynamics，Differential Equations, 43(2007), No. 1, 130-138.

[62]. Y. Lu, Nonstrictly hyperbolic systems with stiff relaxation terms, J. Math. Anal. Appl., 324(2006), 1407-1416.

[61]. Y. Lu, Lower bound estimates for viscosity solutions to isentropic gas dynamics and to Euler equations, J. Math. Anal. Appl., 323(2006), 558-568.

[60]. Y. Lu, Global weak solution for a symmetrically hyperbolic system, Appl. Math. Letters, 19(2006),No.6, 522-526。

[59]. Y. Lu, Existence of global entropy solutions to a nonstrictly   hyperbolic system, Arch. Rat. Mech. Anal., 178 (2005) 287-299.

[58]. Y. Lu and C. Klingenberg, Viscosity and relaxation approximations of hyperbolic-elliptic mixed type system, Proc. A.M.S., 132(2004), No. 5, 1305-1309.

[57]. Y. Lu and C. Klingenberg, A mixed type system of three equations modelling reaction flows,  Proc. A.M.S., 131(2003), 11, 3511-3516.

[56]. C. Klingenberg, Y. Lu and L. Rendon, The global Lipchitz-continuous solutions of isentropic gas dynamics, Applicable Analysis, 82(2003), 1, 35-43.

[55]. C.Klingenberg, Y. Lu and H.J. Zhao, $L1$-singular limit for the relaxation and viscosity approximations, Electron. J. Diff. Eqns., Vol. 2003, No. 23, 1-11.

[54]. Y. Lu and L. Qian, Regularity of viscosity solutions of a degenerate parabolic equation, Proceedings of A.M.S., 130(2002), 999-1004.

[53]. Y. Lu, H\"older estimates of solutions on a degenerate diffusion equation, Proceedings of A.M.S., 130(2002), 1339-1343.

[52]. Y. Lu, Relaxation limit for hyperbolic systems in chromatography, Proceedings of A.M.S., 130(2002), 3579-3583.

[51]. Y. Lu, I. Mantilla and L. Rendon, Holder estimates of solutions on the equation $u_{t}= \Delta G(u)$, Applicable Analysis, 81(2002), 333-339.

[50]. Y. Lu, Singular limits of stiff relaxation and dominant diffusion for nonlinear systems, J. Diff. Equs. 179(2002), No. 2, 687-713.

[49]. F. Caicedo, Y. Lu and M. Sepulveda, Relaxation approximations and BV estimates for some partial differential equations, Electron. J. Diff. Equs., Vol. 2002(2002), No. 19, pp. 1-10.

[48]. Y.Lu and W. Jaeger, On solutions to nonlinear reaction diffusion convection equations with degenerate diffusion, J. Diff. Equas., 170 (2001), No. 1, 1-21.

[47]. Y. Lu and M. Sepulveda, Artificial and physical viscosity solutions for a hyperbolic conservation system, Applicable Analysis, 78(2001), 33-42.

[46]. Y. Lu, I. Mantilla and L. Rendon, Convergence of approximated solutions to nonstrictly hyperbolic system, Advanced Nonlinear Studies, 1(2001), 65-79.

[45]. Y. Lu and C. Klingenberg, The relaxation limits for systems of Broadwell type, Differential and Integral Equations, Vol. 14(2001), No.1, 117-127.

[44].Y. Lu, Holder estimates of solutions of biological population equations, Appl. Math. Letters, 13(2000), 123-126.

[43]. Y. Lu, Holder estimates of solutions of some doubly nonlinear degenerate parabolic equations, Communcation in P.D.E., 24(1999), 5&6, 895-914.          

[42].Y. Lu, P. Sweby and K. Chen, The rate of convergence of the viscosity method for a nonlinear hyperbolic system, Nonlinear Analysis, 38(1999), 4: 435-445.

[41]. C. Klingenberg and Y. Lu, The vacuum case in Diperna's paper, J. Math. Anal. Appl. 1225(1998),679-684.

[40]. Y. Lu, Existence of global solutions for viscoelastic systems, J. Math. Anal. Appl.. 218(1998), 175-182.

[39]. Y. Lu and C. Klingenberg, Existence of solutions to hyperbolic conservation laws with a source, Commun. Math. Phys., 187(1997), 327-340.

[38]. W Jaeger and Y. Lu, Global regularity of solutions for general degenerate parabolic equations in 1-D, J. Diff. Equs., 140(1997), 365-377.

[37]. Y.Lu, Z.Wang, C.Zhu and H.Zhao, Convergence of the viscosity method for a nonstrictly hyperbolic system, J. Sys. Sci. & Math. Scis., 16(1996), 1: 36-47.

[36]. Y. Lu, Existence of generalized solutions for some coupled systems of nonlinear hyperbolic equations, J. Sys. Sci. & Math. Scis., 16(1996),4: 125-135.

[35]. Y. Lu and B. Xuan, Riemann problem on some hyperbolic PDEs (in Chinese), Acta Math. Sci., 16(1996), 187-194.

[34]. C. Klingenberg and Y. Lu, Cauchy problem for hyperbolic conservation laws with a relaxation term, Proc. Roy. Soc. Edin. 126(1996), 821-828.

[33]. Y. Lu and C. Klingenberg, The Cauchy problem for hyperbolic conservation laws with three equations, J. Math. Appl. Anal., 202(1996), 206-216.

[32]. Y. Lu, The Cauchy problem for reaction-convection equations in higher-dimensional spaces, Acta Math. Sci., 14(1994), 3:332-336

[31]. Y. Lu, Convergence of the viscosity method for some nonlinear hyperbolic systems, Proc. Roy. Soc. Edin. 124A(1994), 341-352

[30]. Y. Lu, Cauchy problem for a hyperbolic model, Nonlinear Analysis, TMA, 23(1994), 9: 1135-1144  

[29]. Y. Lu, Global Holder continuous solutions of nonstrictly hyperbolic systems, J. Partial Diff. Equs., 7(1994),132-142

[28]. Y. Lu, Global Holder continuous solution of isentropic gas dynamics, Proc. Roy. Soc. Edin. 123A(1993), 231-238

[27]. Y. Lu, C.Zhu and H. Zhao, Viscous solutions of quadratic conservation laws with umbilic points, Nonlinear Analysis, TMA. 21(1993), 7, 485-499

[26]. Y. Lu, Global classical solution of the Cauchy problem for two-dimensional gas dynamics system, Acta Math. Sci., 13(1993),1: 65-73  

[25]. Y. Lu and J. Hu, Existence of generalized solutions to a hyperbolic model of combustion, Acta Math. Sci., 13(1993), 2:195-201

[24]. Y. Lu and C. Zhu, Existence and asymptotic behavior of solutions to inhomogeneous 2 by 2 hyperbolic quadratic conservation laws with small viscosity, J. Sys. Sci. & Math.Scis. 13(1993), 297-304

[23]. Y. Lu, Convergence of the viscosity method for a nonstrictly hyperbolic conservation laws, Comm. Math. Phys., 150(1992), 59-64

[22]. Y. Lu, Cauchy problem for an extended model of combustion, Proc. Roy. Soc. Edin. 120A(1992), 349-360

[21]. Y. Lu and J. Wang,The interactions of elementary waves of nonstrictly hyperbolic system, J. Math. Anal. Appl., 166 (1992), 1:136-169

[20]. Y. Lu, Convergence of the viscosity method for a nonstrictly hyperbolic system, Acta Math. Sci., 12(1992), 2:230-239

[19]. Y. Lu, Existence and asymptotic behavior of solutions to inhomogeneous systems of gas dynamics with viscosity, Acta Math. Sci., 12(1992), 1:51-61

[18]. Y. Lu, Existence and asymptotic behavior of solutions to inhomogeneous equations of elasticity with little viscosity, Nonlinear Analysis, TMA. 16(1991) 3:197-207

[17]. Y. Lu and H. Zhao, Existence and asymptotic behavior of solutions to 2 by 2 hyperbolic quadratic conservation laws with viscosity, Nonlinear Analysis, TMA. 17(1991), 2:169-180

[16]. G. Chen and Y. Lu,Convergence of the approximation solutions to isentropic gas dynamics, Acta Math. Sci., 10(1990), 1:39-46

[15]. Y. Lu, Existence and asymptotic behavior of solutions to gas dynamics systems with diferent viscosity coefficients, Chin. Sci. Bull., 35(1990), 9:785-786

[14]. G. Chen and Y. Lu, The study on application way of the compensated compactness theory, Chin. Sci. Bull., 34(1989),1:15-19

[13]. Y. Lu, Convergence of solutions to nonlinear dispersive equations without convexity conditions, Applicable Analysis, 31(1989),4:239-246

[12]. Y. Lu, Asymptotic behavior of solutions of initial problem to systems of gas dynamics with viscous term, Chin. Sci. Bull., 34(1989),1: 7-11

[11]. G. Chen and Y. Lu, Existence of solutions for inhomogeneous systems of gas dynamics, Acta Math. Sci., 9(1989), 2: 121-130

[10]. G. Chen and Y. Lu, A study of approaches to applying the theory of compensated compactness, Kexue-Tongbao (Chinese) ,33 (1988), no. 9, 641--644.

[09]. Y. Lu, Asymptotic behavior of solutions to the gas dynamics equations with a viscosity term, Kexue-Tongbao (Chinese)，33 (1988), no. 1, 4--7.

[08]. Y. Lu and G. Xie, The asymptotic behavior of solutions of initial value problem to system of gas dynamics with viscosity, Acta Math. Sci., 8(1988), 2: 185-198

[07]. G. Chen and Y. Lu, Existence and asymptotic behavior of solutions to systems of gas dynamics with a class of sources, Acta Math.Sci., 8(1988), 1:85-94

[06]. G. Wang, G. Xie and Y. Lu, Existence and asymptotic behavior of global solutions of the Cauchy problem for inhomogeneous systems of isentropic gas motion with viscosity, J. Cent. China Norm. Univ., Nat. Sci. 22, No.2, 129-134 (1988).

[05]. J. Sun and Y. Lu, On the antiblowing-up and antiquenching problems for semilinear parabolic equations, J. Shandong Univ., Nat. Sci.,22, No.2, 26-34 (1987).

[04]. Y. Lu, 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.

[03]. A. Jeffrey and Y. Lu, A study of the global weak solution for the isentropic equations of polytropic gas, AMS/IP Studies in Advanced Mathematics, Volume 3, 1997(261-270).  

[02]. C. Klingenberg and Y. Lu, Existence of solutions to resonant systems of conservation laws, Collection: Hyperbolic problems: theory, numerics, applications (Stony Brook, NY,1994),383--389 World Sci. Publishing, River Edge, NJ, 1996.

[01]. C. Klingenberg and Y. Lu, Cauchy problem for hyperbolic conservation laws with relaxation terms, Matematica Contemporanea, Vol.11, 1996(51-60).

 

主持项目

11.一类非线性抛物方程组整体解的先验估计,(国家自然科学基金面上项目12071106)，主持人，2021.01.01-2024.12.31, 50万元

10.一类非线性双曲方程组解的存在性和大时间性态，(省自然科学基金项目LY20A010023), 主持人，2020-2021, 6万元

9. 浙江省重点学科“基础数学”, 主持人，250万, 2013-2021

8. 非线性双曲守恒律和补偿列紧理论（国家自然科学基金面上项目11271105），主持人，2013-2016, 68 万元

7. 补偿列紧理论在非线性双曲守恒律中的应用，(省自然科学基金

项目LY12A01030), 主持人，2012-2013, 6万元

6. 中科院百人计划项目《非线性双曲守恒律的研究》,200万元,主持人，2001-2010                  

5. 中科院院长特别基金《补偿列紧理论与松驰现象》，9万元，主持人，1997-1999

4. 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，主持人，1993-1995

3. 中科院留学择优支持基金《补偿列紧理论的应用》，2万元，主持人，1993

2. 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

1. 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

 

成果：

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，独立

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，独立

5. 论文Existence of Global Entropy Solutions to a Nonstrictly Hyperbolic System被评为安徽省第五届自然科学优秀学术论文一等奖，2007年1月，省级，独立

6. 1993年起享受政府特殊津贴

7. 2009年获江苏省五一劳动荣誉奖章

8. 2011年起入选浙江省特聘专家

9. 2011年获中国科学院"优秀研究生指导教师"奖(培养的博士获中国科学院优秀博士论文奖、国家优秀博士论文提名奖)

10. 2012年获杭州市自然科学优秀学术成果奖一等奖(1/1)

11. 2012年获浙江省自然科学学术奖一等奖(1/2)

12. 2012年获浙江省高校自然科学成果奖二等奖(1/1)

13. 2016年入选浙江省钱江特聘教授

14. 2017年成果《补偿列紧理论及相关双曲方程组的研究》获浙江省人民政府自然科学奖三等奖， 完成人：陆云光、胡燕波

 

其他：

学术服务

1. 1997年元月起任中国《数学物理学报》中、英文版编委

2. 2007年6月始为哥伦比亚国家科学院院士

3. 国家自然科学基金重点项目通讯评审专家

4. Arch. Rat. Mech. Anal., SIAM, JDE等一流杂志审稿人