Yifeng YuProfessor, Mathematics 
Research Interests 
Partial differential equations  
Appointments 
1. Postdoctoral fellow, Mathematical Sciences Research Institute in Berkeley, Aug 2005Dec 2005 2. Instructorship, University of Texas at Austin. Aug 2005Aug 2008. 3. Postdoctoral fellow, Mathematical Sciences Research Institute in Berkeley, July 20 2007Aug 13 2007. 

Publications  [44] Rate of convergence in periodic homogenization of HamiltonJacobi equations: the convex setting (with H. Mitake, H. Tran), arxiv.  
[44] A rigidity result for effective Hamiltonians with 3mode periodic potentials (with Hung V. Tran), submitted.  
[43] Minmax formulas and other properties of certain classes of nonconvex effective Hamiltonians (with Jianliang Qian, Hung Tran), to appear in Mathematische Annalen.  
[42] Curvature effect in shear flow: slowdown of turbulent flame speeds with Markstein number (with Jiancheng Lyu, Jack Xin), to appear in Communications in Math Physics.  
[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, nonroundness and flat pieces of the effective burning velocity from an inviscid quadratic HamiltonJacobi 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 HamiltonJacobi equations (joint with Songting Luo, Hung Tran), Arch. Rational Mech. Analysis, 221 (3), pp 1585–1617, 2016.  
[35] Stochastic homogenization of nonconvex HamiltonJacobi 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 HamiltonJacobi equation in the modeling of traffic flow on a homogeneous signalized road (joint with Wenlong Jin), J. Math. Pure Appl., 104(5), 2015, Pages 9821004.  
[33] Stochastic homogenization of a nonconvex HamiltonJacobi 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 Gequation 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 Gequation 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 Gequation Models in Unsteady Cellular Flows (with Y. Liu, Jack Xin), Math Model. Natural Phenom., 8(3), pp. 198205, 2013.  
[29] Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid HamiltonJacobi models, (with Jack Xin), Annales I’Institut H. Poincare Analyse non lineaire. 30(6), pp. 10491068, 2013.  
[28] A Numerical Study of Turbulent Flame Speeds of Curvature and Strain Gequations in Cellular Flows, (with Y. Liu, Y. Yu), Physica D, 243(1), pp. 2031, 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 HamiltonJacobi equations (joint with Songting Luo, Hongkai Zhao), Multiscale Modeling and Simulation (MMS), Vol. 9 Issue 2, 711734 (2011). 

[24] Asymptotics for turbulent flame speeds of the viscous Gequation enhanced by cellular and shear flows (joint with Jack Xin, Yuyu Liu), Arch. Rational. Mechanics. Anal, 199(2), pp 527561 (2011). 

[23] Periodic homogenization of Gequations and viscosity effects (with Yuyu Liu, Jack Xin), Nonlinearity,23(2010), pp 23512367..  
[22] Homogenization of generalized characteristics associated to solutions of timedependent HamiltonJacobi equations, Asymptotic Analysis, Volume 69, Number 12/2010, page 99116.  
[21] Periodic Homogenization of Inviscid Gequation for Incompressible Flows (with J. Xin), Comm Math Sciences, Vol.8, No. 4, pp10671078, 2010.  
[20] Bounds on Front Speeds for Inviscid and Viscous Gequations (with J. Nolen, J. Xin), Methods and Applications of Analysis, Vol 16, No.4, pp 507520, 2009.  
[19] Mather measures selected by an approximation scheme, (with Diogo Gomes, Renato Iturriaga, Hector SanchezMorgado), 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. 12, 6374.  
[17] Dynamics of propagation of singularities of semiconcave functions, (with P. Cannarsa), J. Eur. Math. Soc (JEMS), 11 (2009), no. 5, 9991024.  
[16] Uniqueness of values of Aronsson operators and applications to game theory, Annales I’Institut H. Poincare Analyse non lineaire, 26 (2009), no. 4, 12991308.  
[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 CarnotCaratheodory spaces, (with Changyou Wang), Illinois J. Math. 52 (2008), no. 3, 757772.  
[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] C1regularity of the Aronsson equation in R2, (with Changyou wang), Annales I’Institut H. Poincare Analyse non lineaire, 25 (2008) 659678.  
[10] Singular set of a convex potential in two dimensions, Comm. Partial Differential Equations, 32 (2007), no. 1012, 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, 14491454.  
[7] Some properties of the infinity ground state, Indiana University Mathematics Journal. 56 No. 2 (2007), 947964.  
[6] A remark on the C 2 solution of the infinity Laplacian equation, Electron. J. Diff. Eqns, Vol. 2006, No. 122, pp. 14.  
[5] A simple proof of the propagation of singularities for solutions of HamiltonJacobi equations, Ann. Sc. Norm. Super. Pisa. Cl. Sci. (5). 2006, 439444.  
[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. 79, 10271046.  
[3] L variational problems and Aronsson equations, Arch. Rational. Mechanics. Anal, 182 (2006), no. 1, 153180.  
[2] Various properties of solutions to the infinity Laplacian equation, (with L.C. Evans). Comm. Partial Differential Equations, 30 (2005), no. 79, 1401–1428.  
[1] Tangent lines of contact for the Infinity Laplacian, Calc. Var. Partial Differential Equations, 21 (2004), no. 4, 349–355  
Grants  NSF collaborative research grant 0601403, 07/01/200606/30/2009. (PI, $78,000). Title: Linfinity variational problems and the Aronsson equation.  
NSF grant 0901460, 06/01/200905/31/2013. (PI, $332,771). Title: Problems related to the infinity Laplacian operator, the weak KAM theory and singularities of solutions of MongeAmpere equations.  
NSF CAREER award 1151919, July 2012June 2017, $400,003, Analysis of Gequations in the modeling of turbulent flame speed and comparison with other math models.  
Link to this profile  http://www.faculty.uci.edu/profile.cfm?faculty_id=5707  
Last updated  01/10/2018  