主要学术贡献

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,XiaojingExistenceanduniquenessofsolutionsforaclassofnon-Newtonianfluidswithsingularityandvacuum.J.DifferentialEquations245(2008),no.10,2871--2916.2.Lian,Songzhe;Yuan,Hongjun;Cao,Chunling;Gao,Wenjie;Xu,XiaojingOntheCauchyproblemfortheevolution$p$-Laplacianequationswithgradienttermandsource.J.DifferentialEquations235(2007),no.2,544--585.3.Lei,Yutian;Wu,Zhuoqun;Yuan,HongjunRadialminimizersofaGinzburg-Landaufunctional.Electron.J.DifferentialEquations1999,No.30,21pp.4.Wu,Zhuoqun;Yuan,Hongjun;Yin,JingxueSomepropertiesofsolutionsforasystemofdynamicsofbiologicalgroups.Comm.PartialDifferentialEquations22(1997),no.9-10,1389--1403.5.Yuan,HongJun,Höldercontinuityofinterfacesfortheporousmediumequationwithabsorption.Comm.PartialDifferentialEquations18(1993),no.5-6,965--976.6.Yuan,Hongjun;Wang,ChangjiaUniquesolvabilityforaclassoffullnon-Newtonianfluidsofonedimensionwithvacuum.Z.Angew.Math.Phys.60(2009),no.5,868--898.35Q357.Yin,Li;Xu,Xiaojing;Yuan,HongjunGlobalexistenceanduniquenessofsolutionoftheinitialboundaryvalueproblemforaclassofnon-Newtonianfluidswithvacuum.Z.Angew.Math.Phys.59(2008),no.3,457--474.8.Xu,Xiaojing;Yuan,HongjunExistenceoftheuniquestrongsolutionforaclassofnon-Newtonianfluidswithvacuum.Quart.Appl.Math.66(2008),no.2,249--279.9.Wang,Changjia;Yuan,HongjunGlobalstrongsolutionsforaclassofheat-conductingnon-Newtonianfluidswithvacuum.NonlinearAnal.RealWorldAppl.11(2010),no.5,3680–3703,10.Lining,Tong;Hongjun,YuanClassicalsolutionstoNavier-Stokesequationsfornonhomogeneousincompressiblefluidswithnon-negativedensities.J.Math.Anal.Appl.362(2010),no.2,476–504.11.Lian,Songzhe;Gao,Wenjie;Cao,Chunling;Yuan,HongjunStudyofthesolutionstoamodelporousmediumequationwithvariableexponentofnonlinearity.J.Math.Anal.Appl.342(2008),no.1,27--38.12.Lian,Songzhe;Yuan,Hongjun;Cao,Chunling;Gao,WenjieThelimitingproblemofthedrift-diffusion-Poissonmodelwithdiscontinuous$p$-$n$-junctions.J.Math.Anal.Appl.347(2008),no.1,157--168.13.Yuan,Hongjun;Chen,MingtaoPositivesolutionsforaclassof$p$-Laplaceproblemsinvolvingquasi-linearandsemi-linearterms.J.Math.Anal.Appl.330(2007),no.2,1179--1193.14.Xin,Zhouping;Yuan,HongjunVacuumstateforsphericallysymmetricsolutionsofthecompressibleNavier-Stokesequations.J.HyperbolicDiffer.Equ.3(2006),no.3,403--442.15.Yuan,Hongjun;Tong,Lining;Xu,XiaojingBVsolutionsfortheCauchyproblemofaquasilinearhyperbolicequationwith$\sigma$-finiteBorelmeasureandnonlinearsource.J.Math.Anal.Appl.311(2005),no.2,715--735.16.Yuan,Hongjun;Xu,Xiaojing;Gao,Wenjie;Lian,Songzhe;Cao,ChunlingExtinctionandpositivityfortheevolution$p$-Laplacianequationwith$L^1$initialvalue.J.Math.Anal.Appl.310(2005),no.1,328--337.17.Hongjun,Yuan;Songzhe,Lian;Wenjie,Gao;Xiaojing,Xu;Chunling,CaoExtinctionandpositivityfortheevolution$p$-Laplacianequationin$R^n$.NonlinearAnal.60(2005),no.6,1085--1091.18.Hongjun,Yuan;Xiaoyu,ZhengExistenceanduniquenessforaquasilinearhyperbolicequationwith$\sigma$-finiteBorelmeasuresasinitialconditions.J.Math.Anal.Appl.277(2003),no.1,27--50.19.Yuan,HongjunTheCauchyproblemforasingularconservationlawwithmeasuresasinitialconditions.J.Math.Anal.Appl.225(1998),no.2,427--439.20.Hongjun,YuanSource-typesolutionsofasingularconservationlawwithabsorption.NonlinearAnal.32(1998),no.4,467--492.21.Yuan,HongJunExtinctionandpositivityfortheevolution$p$-Laplacianequation.J.Math.Anal.Appl.196(1995),no.2,754--763.22.Yuan,HongJunTheCauchyproblemforaquasilineardegenerateparabolicsystem.NonlinearAnal.23(1994),no.2,155--164.23.Yuan,HongJunFinitevelocityofthepropagationofperturbationsforgeneralporousmediumequationswithstrongdegeneracy.NonlinearAnal.23(1994),no.6,721--729.24.Yuan,HongjunContinuityofweaksolutionsforquasilinearparabolicequationswithstrongdegeneracy.Chin.Ann.Math.Ser.B28(2007),no.4,475--498.25.Yuan,HongJun;Lian,SongZhe;Cao,ChunLing;Gao,WenJie;Xu,XiaoJingExtinctionandpositivityforadoublynonlineardegenerateparabolicequation.ActaMath.Sin.(Engl.Ser.)23(2007),no.10,1751--1756.26.Yuan,HongJun;Tong,LiNingBVsolutionsforaquasilinearhyperbolicequationwithnonlinearsourceandfiniteRadonmeasuresasinitialconditions.(Chinese)ActaMath.Sci.Ser.AChin.Ed.30(2010),no.1,54–70,27.Yuan,Hongjun;Wang,ShuThezero-Machlimitofaclassofcombustionflow.J.PartialDiffer.Equ.22(2009),no.4,362–375,28.Ren,ChangYu;Guan,JinRui;Yuan,HongJunAclassofgeneral-formparabolicMonge-Ampèreequations.(Chinese)ChineseAnn.Math.Ser.A30(2009),no.3,421--432.35K9629.Yuan,Hongjun;Yan,HanExis