主要學(xué)術(shù)貢獻(xiàn)

1、主要學(xué)術(shù)貢獻(xiàn)主要從事非線性偏微分方程的研究，著重探討流體動力學(xué)等領(lǐng)域中的數(shù)學(xué)理論及其應(yīng)用。多次應(yīng)邀到美國、香港和新加坡等地學(xué)術(shù)訪問或演講。主持或參加了多個科研項目，在國內(nèi)外學(xué)術(shù)刊物發(fā)表論文60 余篇。主講高等數(shù)學(xué)，數(shù)學(xué)物理方程，偏微分方程泛函方法，流體動力學(xué)的數(shù)學(xué)理論，非線性偏微分方程的某些理論。指導(dǎo)博士研究生11 人，其中9 人已經(jīng)畢業(yè)并獲得博士學(xué)位。指導(dǎo)碩士研究生26 人，其中20 人已經(jīng)畢業(yè)并獲得碩士學(xué)位。合作編寫教材數(shù)學(xué)物理方程一部，已由高等教育出版社出版。獲獎勵情況(1) 1999 年獲得教育部科學(xué)技術(shù)進(jìn)步一等獎；(2) 2000 年獲得教育部首屆青年教師獎；(3) 2002 年獲得

2、吉林省第七屆青年科技獎；(4) 2006 年獲得吉林省長春市政府特殊津貼。科研項目1) “相變和圖像處理等領(lǐng)域中的某些非線性擴(kuò)散方程”， 教育部優(yōu)秀青年教師教學(xué)與科研獎勵基金項目，項目負(fù)責(zé)人,2000 2004；2) “圖像處理中的非線性擴(kuò)散模型”， 國家自然科學(xué)基金項目青年基金項目，項目負(fù)責(zé)人 ,2001 2003；3) “流體動力學(xué)等領(lǐng)域中的具有退化性或奇異性的某些數(shù)學(xué)模型”， 國家自然科學(xué)基金面上項目，項目負(fù)責(zé)人,2006 2008；4)“數(shù)學(xué)與其它領(lǐng)域交叉的若干專題”，國家重點基礎(chǔ)研究發(fā)展計劃973 計劃，參加者，2006 2011；5) “帶有奇異性的某些流體動力學(xué)模型”, 國家自然

3、科學(xué)基金面上項目，項目負(fù)責(zé)人，2010年2012年。發(fā)表論文目錄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