## 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

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

**Appointments**

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.

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.

Publications

[45] Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex setting (with H. Mitake, H. Tran), submitted.

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[44] A rigidity result for effective Hamiltonians with 3-mode periodic potentials (with Hung V. Tran), submitted, to appear in Advances in Mathematics.

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[43] Min-max formulas and other properties of certain classes of nonconvex effective Hamiltonians (with Jianliang Qian, Hung Tran), to appear in Mathematische Annalen.

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[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.

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[41] Computing Residual Diffusivity by Adaptive Basis Learning via Spectral Method (with Jiancheng Lyu, Jack Xin), Numerical Mathematics: Theory, Methods & Applications, 2017, to appear.

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[40] Performance analysis and signal design for a stationary signalized ring road (joint with Wenlong Jin), submitted.

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[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.

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[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.

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[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.

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[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.

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[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.

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[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.

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[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.

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[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.

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[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.

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[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.

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[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.

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[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.

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[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.

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[26] $C^1$-boundary regularity of planar infinity harmonic functions (with Changyou Wang), Math. Res. Lett. 19 (2012), no. 4, 823–835.

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[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).

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).

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[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).

and shear flows (joint with Jack Xin, Yu-yu Liu), Arch. Rational. Mechanics. Anal, 199(2), pp 527-561 (2011).

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[23] Periodic homogenization of G-equations and viscosity effects (with Yu-yu Liu, Jack Xin), Nonlinearity,23(2010), pp 2351-2367..

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[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.

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[21] Periodic Homogenization of Inviscid G-equation for Incompressible Flows (with J. Xin), Comm Math Sciences, Vol.8, No. 4, pp1067-1078, 2010.

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[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.

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[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.

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[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.

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[17] Dynamics of propagation of singularities of semiconcave functions, (with P. Cannarsa), J. Eur. Math. Soc (JEMS), 11 (2009), no. 5, 999-1024.

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[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.

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[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.

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[14] Uniqueness and Nonuniqueness of viscosity solutions of Aronsson equations, (with Robert Jensen, Changyou Wang), Arch. Rational. Mechanics. Anal, 2008, no. 2, 347–370.

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[13] Aronsson’s equations on Carnot-Caratheodory spaces, (with Changyou Wang), Illinois J. Math. 52 (2008), no. 3, 757--772.

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[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.

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[11] C1-regularity of the Aronsson equation in R2, (with Changyou wang), Annales I’Institut H. Poincare- Analyse non lineaire, 25 (2008) 659-678.

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[10] Singular set of a convex potential in two dimensions, Comm. Partial Differential Equations, 32 (2007), no. 10-12, 1883–1894.

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[9] L variational problems and weak KAM theory, Comm. Pure Appl. Math, Vol. 60 (2007), no. 8, 1111–1147.

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[8] A remark on the semiclassical measure, Proc. Amer. Math. Soc. 135 (2007), no. 5, 1449-1454.

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[7] Some properties of the infinity ground state, Indiana University Mathematics Journal. 56 No. 2 (2007), 947-964.

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[6] A remark on the C 2 solution of the infinity Laplacian equation, Electron. J. Diff. Eqns, Vol. 2006, No. 122, pp. 1-4.

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[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.

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[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.

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[3] L variational problems and Aronsson equations, Arch. Rational. Mechanics. Anal, 182 (2006), no. 1, 153-180.

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[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.

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[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, 07/01/2006-06/30/2009. (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.

**Link to this profile**

**Last updated**

06/22/2018