Dr. Tong LI

Professor

Department of Mathematics

The University of Iowa

Iowa City, IA 52242 USA

 
Office: 1A MLH
Email: tong-li@uiowa.edu
Phone: 319-335-3342
Fax: 319-335-0627
Paper Mail

Dr. Tong LI
Department of Mathematics
15 MLH
The University of Iowa
Iowa City, IA 52242-1419
USA

Curriculum Vitae

CV

Teaching Spring, 2023, MATH:3550 Eng. Math. V

Educational Background:

Ph. D. in Mathematics, May, 1992, Courant Institute of Mathematical Sciences, New York University.
M.S. in Mathematics, February, 1990, Courant Institute of Mathematical Sciences, New York University.
M. S. in Mathematics, July, 1986, Peking University , Beijing, China
B. A. in Mathematics, July, 1983, Peking University , Beijing, China

Academic Experience:

2008-current, Professor, Department of Mathematics, The University of Iowa.
1999-2008, Associate Professor, Department of Mathematics, The University of Iowa.
2000-current, A Faculty Member of Program in Applied Mathematical and Computational Sciences, The University of Iowa.
Iowa Informatics Initiative (UI3) Affiliated faculty, since April 24, 2019.
Fall, 2015, Long term visitor of the Mathematical Biosciences Institute (MBI), The Ohio State University.
Long Term Visitor of the Institute for Pure and Applied Mathematics (IPAM), UCLA, November 15-December 15, 2015.
May-June, 2011, Visiting Professor, University of Hamburg, Germany.
Fall, 2008, Member of the Mathematical Biosciences Institute (MBI), The Ohio State University.
Fall, 2008, Member of the Institute for Mathematics and its Applications(IMA), University of Minnesota.
Spring, 2002, Visiting Member of Institute for Advanced Study, Princeton, New Jersey.
1993-1999, Assistant Professor, Department of Mathematics, University of Iowa.
1995-1997, Assistant Professor in Mathematics, UCLA.
1992-1993, Visiting Member of Institute for Advanced Study, Princeton, New Jersey.

Research Interests:

Nonlinear Hyperbolic Conservation Laws
Shock Waves
Combustion
Traffic Flow
Bio-Mathematics
Numerical Analysis

Selected Publications and Recent Works

Tong Li and Nitesh Mathur, Global well-posedness and asymptotic behavior of BV solutions to a system of balance laws arising in traffic flow, Networks and Heterogeneous Media, 18(2)(2023), 581-600.
Tong Li and Jeungeun Park,Traveling waves in a Keller-Segel model with logistic growth, Communications in Mathematical Sciences, 20(2022), 829-853.
Tong Li and Nitesh Mathur, Riemann Problem For A Non-Strictly Hyperbolic System In Chemotaxis, Discrete and Continuous Dynamical Systems Series B, 27(2022), 2173-2187.
Tong Li and Zhian Wang, Traveling wave solutions to the singular Keller-Segel system with logistic source, Mathematical Biosciences and Engineering, 19((2022), 8107-8131.
Weifeng Jiang, Yuan Zhang, Tong Li and Tingting Chen, The cavitation and concentration of Riemann solutions for the isentropic Euler equations with isothermal dusty gas, Nonlinear Analysis: Real World Applications, 71(2023), 103761.
Weifeng Jiang, Tingting Chen, Tong Li and Zhen Wang, The wave interactions of an improved Aw-Rascle-Zhang model with a non-genuinely nonlinear field, Discrete and Continuous Dynamical Systems Series B, 28(2023), 1528-1552.
Weifeng Jiang, Tingting Chen, Tong Li and Zhen Wang, The Riemann problem with delta initial data for the non-isentropic improved Aw-Rascle-Zhang model, Acta Mathematica Scientia, 43B(1)(2023), 237-258.
Tingting Chen, Weifeng Jiang and Tong Li, On the stability of the improved AwRascle-Zhang model with Chaplygin pressure, Nonlinear Analysis: Real World Applications, 62(2021), p. 103351.
Lihui Guo, Tong Li and Gan Yin, The transition of Riemann solutions of the modified Chaplygin gas equations with friction to the solutions of the Chaplygin gas equations, Zeitschrift f"ur angewandte Mathematik und Mechanik, 102(2022), Issue 3, e201800064000.
Tong Li, Dehua Wang, Fang Wang, Zhian Wang and Kun Zhao, Large time behavior and diffusion limit for a system of balance laws from chemotaxis in Multi-dimensions, Communications in Mathematical Sciences, 19(2021), 229-272.
Weifeng Jiang, Tong Li and Zhen Wang, The Limiting Behavior of the Riemann Solutions of Non-isentropic Modified Chaplygin Gas Dynamics, Journal of Mathematical Physics, 62, 041501(2021).
Weifeng Jiang , Tong Li , Zhen Wang and Tingting Zhang, The Riemann solutions comparison for compressible Euler equations in different Chaplygin gas states, Applicable Analysis,101(2022), 4759-4773. /dd0
Yanbo Hu and Tong Li, Sonic-supersonic solutions for the two-dimensional self-similar full Euler equations, Kinetic & Related Models, 12(2019), 1197-1228.
Tong Li and Jeungeun Park, Traveling waves in a chemotaxis model with logistic growth, Discrete and Continuous Dynamical Systems-B, 24(2019), 6465-6480.
Yanbo Hu and Tong Li, The regularity of a degenerate Goursat problem for the 2-D isothermal Euler equations, Communications on Pure and Applied Analysis, 18(2019), 3317-3336.
Chao Deng and Tong Li, Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces, Discrete and Continuous Dynamical Systems-B, 24(2019), 183-195.
Xiaoyan Wang, Tong Li and Jinghua Yao, Dynamical behaviors of a system modeling wave bifurcations, Communications in Mathematical Sciences, 16(2018), 1869-1894.
Yanbo Hu and Tong Li, An improved regularity result of semi-hyperbolic patch problems for the 2-D isentropic Euler equations, J. Math. Anal. Appl., 467(2018), 1174-1193.
Lijun Pan, Xinli Han, Tong Li, and Lihui Guo, The generalized Riemann problem and instability of delta shock to the chromatography equations, Communications in Mathematical Sciences, 16(2018), 705-734.
Lihui Guo, Tong Li, Lijun Pan and Xinli Han, The Riemann Problem with Delta Initial Data for the One-Dimensional Chaplygin Gas Equations with a Source Term, Nonlinear Analysis: Real World Applications, 41(2018), 588-606.
Tong Li and Jeungeun Park, Stability of traveling wave solutions of models for image processing with non-convex nonlinearity, Communications on Pure and Applied Analysis, 17(2018), 959-985.
Tong Li and Jeungeun Park, Stability of traveling wave solutions of nonlinear conservation laws for image processing, Communications in Mathematical Sciences, 15(2017), 1073-1106.
Tong Li, Hailiang Liu and Lihe Wang, Oscillatory traveling wave solutions to an attractive chemotaxis system, J. Diff. Eqn., 261(2016), 7080-7098.
Tong Li and Kun Zhao, Analysis of non-isentropic compressible Euler equations with relaxation, J. Diff. Eqn., 259(2015), 6338-6367.
Tong Li and Jinghua Yao, Equivariant Hopf bifurcation with arbitrary pressure laws in continuum mechanics, Physica D, 310(2015), 79-94.
Tong Li and Anthony Suen, Existence of intermediate weak solutions to the equations of multi-dimensional chemotaxis systems, Discrete and Continuous Dynamical Systems - Series A, 36(2016), 861-875.
Tong Li, Min Tang and Xu Yang, An augmented Keller-Segal model for E. coli chemotaxis in fast-varying environments, Communications in Mathematical Sciences, 14(2016), 883-891.
Tong Li, Anthony Suen, Michael Winkler and Chuan Xue, Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms, Mathematical models and methods in applied sciences, (2015), 721-746.
Chao Deng and Tong Li, Well-posedness of the 3D Parabolic-hyperbolic Keller-Segel System in the Sobolev Space Framework, J. Diff. Eqn., 257(2014), 1311-1332.
Jingyu Li, Tong Li and Zhi-An Wang, Stability of travelings waves of the Keller-Segel model with logarithmic sensitivity, Mathematical Models and Methods in Applied Sciences, 24(2014), 2819-2849.
T. Li and Hui Yin, Convergence Rate To Strong Boundary Layer Solutions For Generalized BBM-Burgers Equations with Non-convex Flux, Communications on Pure and Applied Analysis, 13(2014), 835-858.
T. Li, Qualitative Analysis of some PDE Models of Traffic Flow, Networks and Heterogeneous Media, 8(2013), 773-781.
T. Li and Zhi-An Wang, Steadily propagating waves of a chemotaxis model, Mathematical Biosciences, 240(2012), 161-168.
T. Li, R.H. Pan and K. Zhao, Global dynamics of a hyperbolic-parabolic model arising from chemotaxis, SIAM J. Appl. Math, 72(2012), 417-443.
T. Li and K. Zhao, Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model, Networks and Heterogeneous Media, 6(2011), 625-646.
D. Li and T. Li, Shock formation in a traffic flow model with arrhenius look-ahead dynamics, Networks and Heterogeneous Media, 6(2011), 681-694.
T. Li and Zhi-An Wang, Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis, J. Diff. Eqn., 250(2011), 1310-1333.
Lina Wang, Yaping Wu and T. Li, Exponential Stability of Large-Amplitude Traveling Fronts for Quasi-linear Relaxation Systems with Diffusion, Physica D, 240(2011), 971-983.
T. Li and K. Zhao, On a quasilinear hyperbolic system in blood flow modeling, Discrete and Continuous Dynamical Systems-B, 16(2011), 333-344.
D. Li, T. Li and K. Zhao, On a hyperbolic-parabolic system modeling chemotaxis, Mathematical Models and Methods in Applied Sciences, 21(2011), 1631-1650.
T. Li and Zhi-An Wang, Nonlinear Stability of Large Amplitude Viscous Shock Waves of a Generalized Hyperbolic-parabolic System Arising in Chemotaxis, Mathematical Models and Methods in Applied Sciences, 20(2010), 1967-1998.
T. Li and Zhi-An Wang, Nonlinear Stability of Traveling Waves to a Hyperbolic-parabolic System Modeling Chemotaxis, SIAM J. Appl. Math., 70(2009), 1522-1541.
T. Li and Suncica Canic, Critical Thresholds in a Quasilinear Hyperbolic Model of Blood Flow, Networks and Heterogeneous Media, 4(2009), 527-536.
T. Li and Hailiang Liu, Critical Thresholds in Hyperbolic Relaxation Systems, J. Diff. Eqn., 247(2009), 33-48.
T. Li and Yaping Wu, Linear and Nonlinear Exponential Stability of Traveling Waves for Hyperbolic Systems with Relaxation, Communications in Mathematical Sciences,, 7(2009), 571-593.
T. Li and Hailiang Liu, Critical Thresholds in a Relaxation System with Resonance of Characteristic Speeds, Discrete and Continuous Dynamical Systems - Series A, 24(2009), 511-521.
T. Li, Y. Li and H. Hethcote, Periodic Traveling Waves in SIRS Endemic Models, Mathematical and Computer Modelling, 49(2009), 393-401.
T. Li, Stability of Traveling Waves in Quasi-Linear Hyperbolic Systems with Relaxation and Diffusion, SIAM J. Math. Anal., 40(2008), 1058-1075.
T. Li and Hailiang Liu, Critical Thresholds in a Relaxation Model for Traffic Flows, Indiana Univ. Math. J., 57(2008), 1409-1431.
T. Li, Nonlinear Dynamics of Traffic Jams, Physica D, 207(2005), 41-51.
T. Li and Hailiang Liu, Stability of a traffic flow model with nonconvex relaxation, Communications in Mathematical Sciences, 3(2005), 101-118.
T. Li, Modelling Traffic Flow with a Time-Dependent Fundamental Diagram, Math. Methods in Appl. Sci., 27(2004), pp. 583-601.
T. Li, Global Solutions of Nonconcave Hyperbolic Conservation Laws with Relaxation Arising from Traffic Flow, J. Diff. Eqn., 190(2003), 131-149.
T. Li, Well-posedness Theory of An Inhomogeneous Traffic Flow Model, Discrete and Continuous Dynamical Systems-B, 2(2002), 401-414.
T. Li and H. M. Zhang, The Mathematical Theory of an Enhanced Nonequilibrium Traffic Flow Model, Network and Spatial Economics, A Journal of Infrastructure Modeling and Computation, Special Double Issue on Traffic Flow Theory, 1(2001), pp. 167-179.
T. Li, Global Solutions And Zero Relaxation Limit For A Traffic Flow Model, SIAM J. Appl. Math., 61(2000), pp. 1042-1061.
T. Li, Rigorous Asymptotic Stability of a CJ Detonation Wave in the Limit of Small Resolved Heat Release, Combustion Theory and Modelling, 1(1997), pp. 259-270.
T. Li's Publications

Recent Presentations and Conferences

Presented a talk at Department of Mathematics at Seoul National University, Korea, December 23, 2022.
Presented an invited talk at Department of Mathematics at Seoul National University, Korea, December 20, 2022.
Presented a talk at the PDE Seminar, November 9, 2022, Department of Mathematics, University of Iowa.
Co-organized an IMA PI Conference, 2022 Iowa PDE Conference, October 22, 2022 at the Department of Mathematics, the University of Iowa.
Attended 86th Midwest PDE Seminar, October 15th-16th, 2022, Columbia, MO.
Gave a talk at Department of Mathematics, ISU, November 1, 2019.
Gave an invited talk at the International Workshop on PDEs and Related, Xinyang Normal University, China, June 27-30, 2019.
Presented a talk at Department of Mathematics, Hangzhou Normal University, China, June 21, 2019.
Presented a talk at Department of Mathematics, Shanghai Normal University, Shanghai, China, June 12, 2019.
Gave a PDE Seminar talk at Department of Mathematics, Oklahoma State University, November 8, 2018.
Gave an invited talk at Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, China, July 10, 2018.
Presented a talk at Department of Mathematics, University of Pittsburgh, October 27, 2017
Presented a colloquium talk at Department of Mathematics, Wayne State University, November 17, 2017.
Presented a colloquium talk at Department of Mathematics, University of Alabama at Birmingham, August 10, 2017.
Presented a talk at Department of Mathematics, Xinjiang University, Urumqi, China, July 24, 2017.
Presented a talk at Institute of Applied Physics, Tsinghua University, Beijing, China, July 5, 2017.
Gave an invited minisymposium talk at the 2nd Annual Meeting of the SIAM Central States Section, September 30-October 2, 2016, at University of Arkansas at Little Rock campus, Arkansas.

Teaching Experience

Calculus for Life Sciences, Vector Calculus, Business Calculus, Differential Equations, Numerical Analysis with MATLAB, Real Analysis, Complex Variables, Linear Algebra, Matrix Algebra, Combinatorics, Partial Differential Equations with MATLAB, Nonlinear Conservation Laws and Shock Wave Theory, Nonlinear Dynamic and Chaos

Professional Service

Associate editor for J. Math. Anal. Appl., 2019-current.
Co-organized an IMA-PI Conference at the Department of Mathematics, the University of Iowa, 2022.
Co-organized 2022 Iowa PDE Seminar at UI, October 30, 2021.
Member of the Honorary Degree Selection Committee, University of Iowa, 2016-2018.
Member of Faculty Senate, 2015-2016.
Member of Association for Women in Mathematics AWM.
Member of the Financial Aid Advisory Charter Committee, University of Iowa, 2013-16.
Member of the Faculty Assembly, College of Liberal Arts and Sciences, University of Iowa, 2008-2011.
Member of the Information Technology Advisory Committee, appointed by the Faculty Senate, University of Iowa, 2012-2015.
Member of the Council on Teaching, appointed by The Faculty Senate, University of Iowa, 2006-2012.
Member of the General Education Curriculum Committee, College of Liberal Arts and Sciences, University of Iowa, 2005-2008.
Member of the Council on the Status of Women, University of Iowa, 2006-2009.
Member of UI Committee on the Celebration of Excellence and Achievement Among Women, 2007-current.
Member of the Executive Committee, Department of Mathematics, University of Iowa, 2009-2011.
Member of the Ph.D qualifying examination committees in the Department of Mathematics, University of Iowa, 2004-current.
Colloquium Chair 04-05, Department of Mathematics, University of Iowa.
Member of Graduate Committee, Department of Mathematics, University of Iowa, 2005-2007.
Member of Council for Diversity, Equity, and Inclusion, Department of Mathematics, University of Iowa, 1996-current. The Department of Mathematics at the University of Iowa has been awarded Presidential Awards for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM) and has won recognition by the AMS Committee on the Profession as Programs that Make a Difference in 2006. Participated as a mentor in the GAANN grant.
Member of Evaluation of Teaching Effectiveness Committee, Department of Mathematics, University of Iowa, 2001-2003.
Member of Undergraduate Committee, Department of Mathematics, University of Iowa, 1998-2001.
Member of the MS comprehensive committees in the Department of Mathematics, University of Iowa, 1998-current.
Member of the Ph. D comprehensive examination committees in the Department of Mathematics, University of Iowa, 2004-current.
Member of Faculty Search Committee, Department of Mechanical Engineering, College of Engineering, University of Iowa, 1994-1996.
Co-organized a Special Session at The AMS 2011 Spring Central Section Meeting at Iowa City, IA, March 18-20, 2011.
Co-organized The Pre-AMS Workshop on PDE Problems at Dept. of Math., UI, Iowa City, IA, March 17-18, 2011.
Co-organized The 2010 Iowa PDE Conference, University of Iowa, April 30-May 2, 2010.
Co-organized a Minisymposium on “Kinetic description, hyperbolic dynamics, and wave propagation“ at the SIAM conference on “Analysis of Partial Differential Equations”, December 7-10, 2009, Miami Florida.
Co-organized Conference on Partial Differential Equations and Their Applications, University of Iowa, July 25-27, 2008
Co-organized the Midwest Geometry Conference May 18 - 20, 2007, University of Iowa.
Co-organized the Midwest PDE Conference, partially sponsored by NSF, September 22-24, 2006, University of Iowa.
Co-organized `The International Nonlinear PDE Conference, University of Iowa, April 1-4, 1999', sponsored partially by IMA, University of Minnesota and NSF.
Co-organized the Annul Sonia Kovalevsky High School Mathematics Day, University of Iowa, 2007-2022.
Attended the 2013 Principal Financial Group Women of Innovation Awards as a finalist, Des Moines, November 21, 2013.

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