主要学术贡献

1、主要学术贡献主要从事非线性偏微分方程的研究，着重探讨流体动力学等领域中的数学理论及其应用。多次应邀到美国、香港和新加坡等地学术访问或演讲。主持或参加了多个科研项目，在国内外学术刊物发表论文60 余篇。主讲高等数学，数学物理方程，偏微分方程泛函方法，流体动力学的数学理论，非线性偏微分方程的某些理论。指导博士研究生11 人，其中9 人已经毕业并获得博士学位。指导硕士研究生26 人，其中20 人已经毕业并获得硕士学位。合作编写教材数学物理方程一部，已由高等教育出版社出版。获奖励情况(1) 1999 年获得教育部科学技术进步一等奖；(2) 2000 年获得教育部首届青年教师奖；(3) 2002 年获得

2、吉林省第七届青年科技奖；(4) 2006 年获得吉林省长春市政府特殊津贴。科研项目1) “相变和图像处理等领域中的某些非线性扩散方程”， 教育部优秀青年教师教学与科研奖励基金项目，项目负责人,2000 2004；2) “图像处理中的非线性扩散模型”， 国家自然科学基金项目青年基金项目，项目负责人 ,2001 2003；3) “流体动力学等领域中的具有退化性或奇异性的某些数学模型”， 国家自然科学基金面上项目，项目负责人,2006 2008；4)“数学与其它领域交叉的若干专题”，国家重点基础研究发展计划973 计划，参加者，2006 2011；5) “带有奇异性的某些流体动力学模型”, 国家自然

3、科学基金面上项目，项目负责人，2010年2012年。发表论文目录1. Yuan, Hongjun; Xu, Xiaojing Existence and uniqueness of solutions for a class of non-Newtonian fluids with singularity and vacuum. J. Differential Equations 245 (2008), no. 10, 2871-2916.2. Lian, Songzhe; Yuan, Hongjun; Cao, Chunling; Gao, Wenjie; Xu, Xiaojing Onth

4、e Cauchy problem for the evolution $p$-Laplacian equations with gradient term and source. J. Differential Equations 235 (2007), no. 2, 544-585.3. Lei, Yutian; Wu, Zhuoqun; Yuan, Hongjun Radial minimizers of a Ginzburg-Landau functional. Electron. J. Differential Equations1999, No. 30, 21 pp.4. Wu, Z

5、huoqun; Yuan, Hongjun; Yin, Jingxue Some properties of solutions for a system of dynamics of biological groups. Comm.P artial Differential Equations 22 (1997), no. 9-10, 1389-1403.5. Yuan, Hong Jun, H?lder continuity of interfaces for the porous mediume quation with absorption. Comm. Partial Differe

6、ntial Equations 18 (1993), no. 5-6, 965-976.6. Yuan, Hongjun; Wang, Changjia Unique solvability for a class of full non-Newtonian fluids of one dimension with vacuum. Z. Angew. Math. Phys. 60 (2009), no. 5, 868-898. 35Q357. Yin, Li; Xu, Xiaojing; Yuan, Hongjun Global existence and uniqueness of solu

7、tion of the initial boundary value problem for a class of non-Newtonian fluids with vacuum. Z. Angew. Math. Phys.59 (2008), no. 3, 457-474.8. Xu, Xiaojing; Yuan, Hongjun Existence of the unique strong solution for a class of non-Newtonian fluids with vacuum. Quart. Appl. Math. 66 (2008), no. 2, 249-

8、279.9. Wang, Changjia; Yuan, Hongjun Global strong solutions for a class of heat-conducting non-Newtonian fluids with vacuum. Nonlinear Anal. Real World Appl. 11 (2010), no. 5, 3680- 3703,10. Lining, Tong; Hongjun, Yuan Classical solutions to Navier-Stokes equations for nonhomogeneousincompressible

9、fluids with non-negative densities. J. Math. Anal. Appl. 362 (2010), no. 2,476- 504.11. Lian, Songzhe; Gao, Wenjie; Cao, Chunling; Yuan, Hongjun Study of the solutions to a model porous medium equation with variable exponent of nonlinearity. J. Math. Anal. Appl. 342 (2008), no. 1, 27-38.12. Lian, So

10、ngzhe; Yuan, Hongjun; Cao, Chunling; Gao, Wenjie The limiting problem of the drift-diffusion-Poisson model with discontinuous $p$-$n$-junctions.J. Math. Anal. Appl. 347 (2008), no. 1, 157-168.13. Yuan, Hongjun; Chen, Mingtao Positive solutions for a class of $p$-Laplace problems involving quasi-line

11、ar and semi-linear terms.J. Math. Anal. Appl.330 (2007), no. 2, 1179-1193.14. Xin, Zhouping; Yuan, Hongjun Vacuums tate for spherically symmetric solutions of the compressible Navier-Stokes equations. J. Hyperbolic Differ. Equ. 3 (2006), no. 3, 403-442.15. Yuan, Hongjun; Tong, Lining; Xu, Xiaojing B

12、V solutions for the Cauchy problem of a quasilinear hyperbolic equation with $sigma$-finite Borel measure and nonlinear source. J. Math. Anal. Appl. 311 (2005), no. 2, 715-735.16. Yuan, Hongjun; Xu, Xiaojing; Gao, Wenjie; Lian, Songzhe; Cao, Chunling Extinction and positivity for the evolution $p$-L

13、aplacian equation with $LA1$ initial value. J. Math. Anal. Appl. 310 (2005), no. 1, 328-337.17. Hongjun, Yuan; Songzhe, Lian; Wenjie, Gao; Xiaojing, Xu; Chunling, Cao Extinction and positivity for the evolution $p$-Laplacian equation in $RAn$. Nonlinear Anal. 60 (2005), no. 6, 1085-1091.18. Hongjun,

14、 Yuan; Xiaoyu, Zheng Existence and uniqueness for a quasilinear hyperbolic equation with $sigma$-finite Borel measures as initial conditions. J. Math. Anal. Appl. 277 (2003), no. 1, 27-50.19. Yuan, Hongjun The Cauchy problem for a singular conservation law with measures as initial conditions. J. Mat

15、h. Anal. Appl. 225 (1998), no. 2, 427-439.20. Hongjun, Yuan Source-type solutions of a singular conservation law with absorption. Nonlinear Anal. 32 (1998), no. 4, 467-492.21. Yuan, Hong Jun Extinction and positivity for the evolution $p$-Laplacian equation. J. Math. Anal. Appl. 196 (1995), no. 2, 7

16、54-763.22. Yuan, Hong Jun The Cauchy problem for a quasilinear degenerate parabolic system. Nonlinear Anal. 23 (1994), no. 2, 155-164.23. Yuan, HongJun Finite velocity of the propagation of perturbations for general porous medium equations with strong degeneracy. Nonlinear Anal. 23 (1994), no. 6, 72

17、1-729.24. Yuan, Hongjun Continuity of weak solutions for quasilinear parabolic equations with strong degeneracy. Chin. Ann. Math. Ser. B 28 (2007), no. 4, 475-498.25. Yuan, Hong Jun; Lian, Song Zhe; Cao, Chun Ling; Gao, Wen Jie; Xu, Xiao Jing Extinction and positivity for a doubly nonlinear degenera

18、te parabolic equation. Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 10, 1751-1756.26. Yuan, Hong Jun; Tong, Li Ning BV solutions for a quasilinear hyperbolic equation with nonlinear source and finiteRadon measures as initialconditions.(Chinese) Acta Math. Sci. Ser. A Chin. Ed. 30 (2010), no. 1, 54 70

19、,27. Yuan, Hongjun; Wang, Shu The zero-Mach limit of a class of combustion flow. J. Partial Differ. Equ. 22 (2009), no. 4, 362- 375,28. Ren, ChangYu; Guan, Jin Rui; Yuan, Hong Jun A class of general-form parabolic Monge-Am住 re equations. (Chinese) Chinese Ann. Math. Ser. A 30 (2009), no. 3, 421-432.

20、 35K9629. Yuan, Hongjun; Yan, Han Existence and uniqueness of BV solutions for a class of degenerate Boltzmann equations with measures as initial conditions.J.Partial Differ. Equ. 22 (2009), no. 2, 127-152. 35F2530. Yuan, Hongjun; Xu, Xiaojing Some entropy inequalities for a quasilinear degenerate h

21、yperbolic equation. J. Partial Differential Equations 18 (2005), no. 4, 289-303.31. Yuan, HongJun; Wu, GangQuasilinear degenerate parabolic equation with Dirac measure. (Chinese) Chinese Ann. Math. Ser. A 26 (2005), no. 4, 515-526; translation in Chinese J. Contemp. Math. 26 (2005), no. 3, 291-30232

22、. Yuan, Hongjun; Jin, Yang Existence and uniqueness of BV solutions for the porous mediumequation with Dirac measure as sources. J. Partial Differential Equations 18 (2005), no. 1, 35-58.33. Yuan, Hong Jun; Xu, Xiao Jing Existence and uniqueness of BV solutions for a quasilinear degenerate hyperboli

23、c equation with local finite measures as initial conditions. (Chinese)Chinese Ann. Math. Ser. A 26 (2005), no. 1,39-48; translation in Chinese J. Contemp. Math. 26 (2005), no. 1, 43-5434. Yuan, Hongjun Instantaneous shrinking and localization of functions in $roman Y_lambda(m,p,q,N)$ and their appli

24、cations. Chinese Ann. Math. Ser. B 22 (2001), no. 3, 361-380.35. Yuan, Hongjun Cauchy's problem for degenerate quasilinear hyperbolic equations with measures as initial values. J. Partial Differential Equations 12 (1999), no. 2, 149-178.36. Yuan, Hongjun Localization condition for a nonlinear di

25、ffusion equation. Chinese J. Contemp. Math. 17 (1996), no. 1, 45-58.37. Yuan, Hongjun Existence and nonexistence of interfaces of weak solutions for nonlinear degenerate parabolic systems. J. Partial Differential Equations 9 (1996), no. 2, 177-185.38. Yuan, Hongjun Extinction and positivity for the

26、non-Newtonian polytropic filtration equation. J. Partial Differential Equations9 (1996), no. 2,169-176.39. Yuan, Hong Jun A localization condition for a class of nonlinear diffusion equations. (Chinese) Chinese Ann. Math. Ser. A 17 (1996), no. 1, 47-58.40. Zhao, Junning; Yuan, Hongjun The Cauchy problem of some nonlinear doubly degenerate parabolic equations. Chinese J. Contemp. Math. 16 (1995), no. 2