Professor& Presidential Scholar
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Ph.D, University of Minnesota (1988, Mathematics)

B.S., Xi'an Jiaotong University (1982, Mathematics)


Dr. Yi Li is Professor in the Mathematics and Computer Science Department. Growing up in Northwest China, he received his B.S. degree in 1982 and his Ph.D. in 1988. Dr. Li's research has dealt with nonlinear elliptic and parabolic differential equations, with their applications in Physics, Biology, and Medicine. In particular, his research includes: 1) Investigate the stability of traveling-wave solutions of the nonlinear reaction-diffusion equations. 2) Models for the transmission of an infectious disease in one and two host populations with and without self-regulation are analyzed. 3) Solve the long-standing problem of the exact bifurcation diagram in case nonlinear term is any cubic with real and distinct roots, as well as the exact S-bifurcation problem, related to gas combustion. 4) Give an explicit formula for exponential decay properties of ground states for a class of quasilinear elliptic equations. 5) Study the structure of positive solutions to quasilinear scalar field equation with homogeneous Neumann boundary condition and show the mountain-pass solution develops into a spike-layer solution. 6) Obtain complete structure of 1-periodic solution by means of singularity theory pushing the Abrosetti-Prodi type theorem. 7) Study the Duffing type equation and obtain the exact multiplicity and stability of periodic solutions. 8) Study the Cauchy problem of a cubic reaction system, prove via the renormalization techniques and nonlinear estimates the global dynamics of solutions under mild decay conditions and show the exact large time behavior of solutions which is universal. 9) Study the Hot Spot Conjecture. 10) Publish the first mathematical paper in the world on the uniqueness for bioluminescence tomography. 11) Pulish the first mathematical paper on computed optical tomography.

Dr. Li publishes in well-known publications like, Arch. Rational Mech. Anal., Duke Math. J., Journal of Differential Equations, Commu. PDE, Communications on Pure and Applied Math., Journal de mathématiques pures et appliquées. He was elected AAAS Fellow in 2018 and was named JJC Presidential Scholar in 2022.  


Courses Taught

Carrent courses

Previous courses

Professional Memberships

Member of American Association for the Advancement of Science

Council of Chinese American Deans and Presidents - CCADP
Scholarly Work

G Wang, Y Li, M Jiang, Uniqueness theorems in bioluminescence tomographyMedical physics 31 (8), 2289-2299

Y Li, WM Ni, Radial symmetry of positive solutions of nonlinear elliptic equations in RnCommunications in partial differential equations 18 (5-6), 1043-1054

Y Li, WM Ni, On conformal scalar curvature equations in ℝnDuke mathematical journal 57 (3), 895-924

Y Li, Asymptotic behavior of positive solutions of equation Δu+ K (x) up= 0 in Rn, Journal of differential equations 95 (2), 304-330

ME Gage, Y Li, Evolving plane curves by curvature in relative geometries IIDuke Mathematical Journal 75 (1), 79-98

MK Kwong, Y Li, Uniqueness of radial solutions of semilinear elliptic equationsTransactions of the American Mathematical Society 333 (1), 339-363

H Chen, Y Li, L Wang, Monotone properties of the eigenfunction of Neumann problemsJournal de Mathématiques Pures et Appliquées 130, 112-129

Honors and Awards

2018 Elected Fellow of American Association for the Advancement of Science

2013 Member of Class of the Institute for Management and Leadership in
Education (MLE), Harvard University

2008 Department received the Exemplary Program Award by the American
Mathematical Society (AMS) for its work in recruiting, mentoring and
preparing doctoral students from underrepresented U.S. minorities

2008 Sloan Foundation Special Recognition on “advancing underrepresented
minority students in mathematics, science and engineering”

2005 Presidential Award for Excellence in Science, Mathematics and
Engineering Mentoring (NSF-PAESMEM) to the Department of
Mathematics, University of Iowa

2004 & 2003 Outstanding International Educator by UI International Programs

2001-2011 Sloan Foundation designated minority Ph.D. student mentor

1988 Excellent Ph.D. Thesis Award, School of Mathematics, University of Minnesota