Yifeng Yu

Picture of Yifeng Yu
Professor, Mathematics
School of Physical Sciences
B.S., Nankai University, 1999
Ph.D., U.C. Berkeley, 2005, Mathematics
Phone: (949) 824-0286
Fax: (949) 824-7993
Email: yyu1@math.uci.edu
University of California, Irvine
410G Rowland Hall
Mail Code: 3875
Irvine, CA 92697
Research Interests
Partial differential equations
1. Postdoctoral fellow, Mathematical Sciences Research Institute in Berkeley,
Aug 2005-Dec 2005
2. Instructorship, University of Texas at Austin. Aug 2005-Aug 2008.
3. Postdoctoral fellow, Mathematical Sciences Research Institute in Berkeley,
July 20 2007-Aug 13 2007.
[53] Bifurcation of homogenization and nonhomogenization of the curvature G-equation with shear flows (with Hiroyoshi Mitake, Connor Mooney, Hung V. Tran and Jack Xin), preprint.
[52] Existence of effective burning velocity in cellular flow for curvature G-equation (with Hongwei Gao, Ziang Long, Jack Xin), Preprint.
[51] Differentiability of effective fronts in the continuous setting in two dimensions (with Hung Tran), to appear in International Mathematics Research Notices.
[50] Effective fronts of polygon shapes in two dimensions (with Wenjia Jing, Hung V. Tran), to appear in SIAM Journal on Mathematical Analysis.
[49] Optimal convergence rate for periodic homogenization of convex Hamilton-Jacobi equations (with Hung Tran), to appear in Indiana Univ. Math. J.
[48] High Degeneracy of Effective Hamiltonian in Two Dimensions, Ann. Inst. H. Poincaré Anal. Non Linéaire 39 (2022), no. 1, pp. 201–223.
[47] Effective fronts of polytope shapes (With Wenjia Jing, Hung V. Tran), Minimax Theory and its Applications 05 (2020), No. 2, 347--360.
[46] Remarks on optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form (with X. Guo, H. V. Tran), SN Partial Differential Equations and Applications, 1, Article number: 15 (2020). Dedicated to Hitoshi Ishii on the award of the 1st Kodaira Kunihiko Prize.
[45] Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex setting (with H. Mitake, H. Tran), Arch. Rational Mech. Analysis, 2019, Volume 233, Issue 2, pp 901–934
[44] A rigidity result for effective Hamiltonians with 3-mode periodic potentials (with Hung V. Tran), submitted, Advances in Mathematics, Volume 334, 20 2018, Pages 300-321.
[43] Min-max formulas and other properties of certain classes of nonconvex effective Hamiltonians (with Jianliang Qian, Hung Tran), Mathematische Annalen, 2018, Volume 372, Issue 1–2, pp 91–123.
[42] Curvature effect in shear flow: slowdown of turbulent flame speeds with Markstein number (with Jiancheng Lyu, Jack Xin), Communications in Math Physics, 2018, Volume 359, Issue 2, pp 515–533.
[41] Computing Residual Diffusivity by Adaptive Basis Learning via Spectral Method (with Jiancheng Lyu, Jack Xin), Numerical Mathematics: Theory, Methods & Applications, 2017, to appear.
[40] Performance analysis and signal design for a stationary signalized ring road (joint with Wenlong Jin), submitted.
[39] Spiral Waves, Edge Transport, and Front Speed Enhancement for ABC Flows (joint with Tyler McMillen, Jack Xin and Andrej Zlatos), SIAM J. Appl. Dyn. Syst., 15(3), 1753–1782.
[38] Inverse problems, non-roundness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model (joint with Wenjia Jing and Hung Tran), Nonlinearity, Volume 30, Number 5, 2017.
[37] Periodic orbits of the ABC flow with $A=B=C=1$ (Joint with Jack Xin, Andrej Zlatos), SIAM J. Math. Anal., 48(6), 4087–4093.
[36] Some inverse problems in periodic homogenization of Hamilton-Jacobi equations (joint with Songting Luo, Hung Tran), Arch. Rational Mech. Analysis, 221 (3), pp 1585–1617, 2016.
[35] Stochastic homogenization of nonconvex Hamilton-Jacobi equations in one space dimension (joint with Scott Armstrong, Hung Tran), J. Differential Equations, 261(5), 2016, pp. 2702–2737.
[34] Asymptotic solution and effective Hamiltonian of a Hamilton-Jacobi equation in the modeling of traffic flow on a homogeneous signalized road (joint with Wenlong Jin), J. Math. Pure Appl., 104(5), 2015, Pages 982-1004.
[33] Stochastic homogenization of a nonconvex Hamilton-Jacobi equation (joint with Scott Armstrong, Hung Tran), Calc. Var. Partial Differential Equations, October 2015, Volume 54, Issue 2, pp 1507–1524.
[32] Asymptotic growth rates and strong bending of turbulent flame speeds of G-equation in steady two dimensional incompressible periodic flows (joint with Jack Xin), SIAM J. Math Analysis, 46(4), pp. 2444–2467, 2014.
[31] Front Quenching in G-equation Model Induced by Straining of Cellular Flow (joint with Jack Xin), Arch. Rational. Mechanics. Anal, 214(2014), pp. 1–34.
[30] Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows (with Y. Liu, Jack Xin), Math Model. Natural Phenom., 8(3), pp. 198-205, 2013.
[29] Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid Hamilton-Jacobi models, (with Jack Xin), Annales I’Institut H. Poincare- Analyse non lineaire. 30(6), pp. 1049-1068, 2013.
[28] A Numerical Study of Turbulent Flame Speeds of Curvature and Strain G-equations in Cellular Flows, (with Y. Liu, Y. Yu), Physica D, 243(1), pp. 20-31, 2013. DOI:10.1016/j.physd.2012.09.008.
[27] Nonuniqueness of infinity ground states (with Ryan Hynd and Charles Smart), Calc. Var. Partial Differential Equations, November 2013, Volume 48, Issue 3, pp 545–554.
[26] $C^1$-boundary regularity of planar infinity harmonic functions (with Changyou Wang), Math. Res. Lett. 19 (2012), no. 4, 823–835.
[25] A new approximation for effective Hamiltonians for
homogenization of a class of Hamilton-Jacobi equations (joint with Songting Luo, Hongkai Zhao), Multiscale Modeling and Simulation (MMS), Vol. 9 Issue 2, 711-734 (2011).
[24] Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular
and shear flows (joint with Jack Xin, Yu-yu Liu), Arch. Rational. Mechanics. Anal, 199(2), pp 527-561 (2011).
[23] Periodic homogenization of G-equations and viscosity effects (with Yu-yu Liu, Jack Xin), Nonlinearity,23(2010), pp 2351-2367..
[22] Homogenization of generalized characteristics associated to solutions of time-dependent Hamilton-Jacobi equations, Asymptotic Analysis, Volume 69, Number 1-2/2010, page 99-116.
[21] Periodic Homogenization of Inviscid G-equation for Incompressible Flows (with J. Xin), Comm Math Sciences, Vol.8, No. 4, pp1067-1078, 2010.
[20] Bounds on Front Speeds for Inviscid and Viscous G-equations (with J. Nolen, J. Xin), Methods and Applications of Analysis, Vol 16, No.4, pp 507-520, 2009.
[19] Mather measures selected by an approximation scheme, (with Diogo Gomes, Renato Iturriaga, Hector Sanchez-Morgado), Proceedings of AMS, Volume 138, Number 10, October 2010, Pages 3591–3601.
[18] Maximal and minimal solutions of an Aronsson equation: L variational problems versus the game theory, Calc. Var. Partial Differential Equations 37 (2010), no. 1-2, 63--74.
[17] Dynamics of propagation of singularities of semiconcave functions, (with P. Cannarsa), J. Eur. Math. Soc (JEMS), 11 (2009), no. 5, 999-1024.
[16] Uniqueness of values of Aronsson operators and applications to game theory, Annales I’Institut H. Poincare- Analyse non lineaire, 26 (2009), no. 4, 1299-1308.
[15] Derivation of Aronsson equation for C 1 Hamiltonian, (with M.G. Crandall, Changyou Wang), Trans. Amer. Math. Soc. 361 (2009), no. 1, 103–124.
[14] Uniqueness and Nonuniqueness of viscosity solutions of Aronsson equations, (with Robert Jensen, Changyou Wang), Arch. Rational. Mechanics. Anal, 2008, no. 2, 347–370.
[13] Aronsson’s equations on Carnot-Caratheodory spaces, (with Changyou Wang), Illinois J. Math. 52 (2008), no. 3, 757--772.
[12] Asymptotic behavior of infinity harmonic functions near isolated singularity, (with Ovidius Savin, Changyou Wang), Int. Math. Res. Not, Vol. 2008. no. 6, Art. ID rnm163, 23 pp.
[11] C1-regularity of the Aronsson equation in R2, (with Changyou wang), Annales I’Institut H. Poincare- Analyse non lineaire, 25 (2008) 659-678.
[10] Singular set of a convex potential in two dimensions, Comm. Partial Differential Equations, 32 (2007), no. 10-12, 1883–1894.
[9] L variational problems and weak KAM theory, Comm. Pure Appl. Math, Vol. 60 (2007), no. 8, 1111–1147.
[8] A remark on the semiclassical measure, Proc. Amer. Math. Soc. 135 (2007), no. 5, 1449-1454.
[7] Some properties of the infinity ground state, Indiana University Mathematics Journal. 56 No. 2 (2007), 947-964.
[6] A remark on the C 2 solution of the infinity Laplacian equation, Electron. J. Diff. Eqns, Vol. 2006, No. 122, pp. 1-4.
[5] A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations, Ann. Sc. Norm. Super. Pisa. Cl. Sci. (5). 2006, 439-444.
[4] Generalized cone comparison principle for viscosity solutions of the Aronsson equation and absolute minimizers, (with Ron Gariepy, Changyou Wang), Comm. Partial Differential Equations, 31 (2006), no. 7-9, 1027-1046.
[3] L variational problems and Aronsson equations, Arch. Rational. Mechanics. Anal, 182 (2006), no. 1, 153-180.
[2] Various properties of solutions to the infinity Laplacian equation, (with L.C. Evans). Comm. Partial Differential Equations, 30 (2005), no. 7-9, 1401–1428.
[1] Tangent lines of contact for the Infinity Laplacian, Calc. Var. Partial Differential Equations, 21 (2004), no. 4, 349–355
NSF collaborative research grant 0601403, 07/01/2006-06/30/2009. (PI, $78,000). Title: L-infinity variational problems and the Aronsson equation.
NSF grant 0901460, 06/01/2009-05/31/2013. (PI, $332,771). Title: Problems related to the infinity Laplacian operator, the weak KAM theory and singularities of solutions of Monge-Ampere equations.
NSF CAREER award 1151919, July 2012-Sep 2018, $400,003, Analysis of G-equations in the modeling of turbulent flame speed and comparison with other math models.
NSF grant 2000191, 2020-2023 (PI, $302,742), Analysis of Properties of Effective Hamiltonians with Applications.
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