主要学术贡献

1、精选优质文档-倾情为你奉上主要学术贡献 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)

2、2002年获得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,20002004；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,20012003；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,20062008；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，20062011；5）“带有奇异性的某些流体动力学模型”,国家自然科学基金面

3、上项目，项目负责人，2010年2012年。 发表论文目录1. ; Existence and uniqueness of solutions for a class of non-Newtonian fluids with singularity and vacuum. 2871-2916.2. ; ; ; ; On the Cauchy problem for the evolution $p$-Laplacian equations with gradient term and source. 544-585. 3. ; ; Radial minimizers of a Ginzburg-

4、Landau functional. No. 30, 21 pp.4. ; ; Some properties of solutions for a system of dynamics of biological groups. 1389-1403.5. , Hölder continuity of interfaces for the porous medium equation with absorption. 965-976.6. ; Unique solvability for a class of full non-Newtonian fluids of one dime

5、nsion with vacuum. 868-898. 7. ; ; Global existence and uniqueness of solution of the initial boundary value problem for a class of non-Newtonian fluids with vacuum. 457-474.8. ; Existence of the unique strong solution for a class of non-Newtonian fluids with vacuum. 249-279.9. Wang, Changjia; Yuan,

6、 Hongjun Global strong solutions for a class of heat-conducting non-Newtonian fluids with vacuum. 11 (2010), no. 5, 36803703,10. Lining, Tong; Hongjun, Yuan Classical solutions to Navier-Stokes equations for nonhomogeneous incompressible fluids with non-negative densities. 362 (2010), no. 2, 476504.

7、 11. ; ; ; Study of the solutions to a model porous medium equation with variable exponent of nonlinearity. 27-38. 12. ; ; ; The limiting problem of the drift-diffusion-Poisson model with discontinuous $p$-$n$-junctions. 157-168. 13. ; Positive solutions for a class of $p$-Laplace problems involving

8、 quasi-linear and semi-linear terms. 1179-1193. 14. ; Vacuum state for spherically symmetric solutions of the compressible Navier-Stokes equations. 403-442.15. ; ; BV solutions for the Cauchy problem of a quasilinear hyperbolic equation with $sigma$-finite Borel measure and nonlinear source. 715-735

9、. 16. ; ; ; ; Extinction and positivity for the evolution $p$-Laplacian equation with $L1$ initial value. 328-337.17. ; ; ; ; Extinction and positivity for the evolution $p$-Laplacian equation in $Rn$. 1085-1091. 18. ; Existence and uniqueness for a quasilinear hyperbolic equation with $sigma$-finit

10、e Borel measures as initial conditions. 27-50.19. The Cauchy problem for a singular conservation law with measures as initial conditions. 427-439. 20. Source-type solutions of a singular conservation law with absorption. 467-492. 21. Extinction and positivity for the evolution $p$-Laplacian equation

11、. 754-763.22. The Cauchy problem for a quasilinear degenerate parabolic system. 155-164. 23. Finite velocity of the propagation of perturbations for general porous medium equations with strong degeneracy. 721-729. 24. Continuity of weak solutions for quasilinear parabolic equations with strong degen

12、eracy. 475-498. 25. ; ; ; ; Extinction and positivity for a doubly nonlinear degenerate parabolic equation. 1751-1756.26. Yuan, Hong Jun; Tong, Li Ning BV solutions for a quasilinear hyperbolic equation with nonlinear source and finite Radon measures as initial conditions. (Chinese) 30 (2010), no. 1

13、, 5470, 27. Yuan, Hongjun; Wang, Shu The zero-Mach limit of a class of combustion flow. 22 (2009), no. 4, 362375, 28. ; ; A class of general-form parabolic Monge-Ampère equations. (Chinese) 421-432. 29. ; Existence and uniqueness of BV solutions for a class of degenerate Boltzmann equations wit

14、h measures as initial conditions. 127-152. 30. ; Some entropy inequalities for a quasilinear degenerate hyperbolic equation. 289-303. 31. ; Quasilinear degenerate parabolic equation with Dirac measure. (Chinese) 26 (2005), 515-526; translation in 26 (2005), 291-302 32. ; Existence and uniqueness of

15、BV solutions for the porous medium equation with Dirac measure as sources. 35-58. 33. ; Existence and uniqueness of BV solutions for a quasilinear degenerate hyperbolic equation with local finite measures as initial conditions. (Chinese) 26 (2005), 39-48; translation in 26 (2005), 43-54 34. Instanta

16、neous shrinking and localization of functions in $roman Y_lambda(m,p,q,N)$ and their applications. 361-380.35. Cauchy's problem for degenerate quasilinear hyperbolic equations with measures as initial values. 149-178. 36. Localization condition for a nonlinear diffusion equation. 45-58. 37. Exis

17、tence and nonexistence of interfaces of weak solutions for nonlinear degenerate parabolic systems. 177-185.38. Extinction and positivity for the non-Newtonian polytropic filtration equation. 169-176. 39. A localization condition for a class of nonlinear diffusion equations. (Chinese) 47-58. 40. ; Th

18、e Cauchy problem of some nonlinear doubly degenerate parabolic equations. 173-192. 41. ; The Cauchy problem for a class of nonlinear doubly degenerate parabolic equations. (Chinese) 181-196. 42. ; Uniqueness of generalized solutions for a quasilinear degenerate parabolic system. 89-96. 43. Regularity of free boundary for certai