Yuan Gao, William W. Elliott Assistant Research Professor of Mathematics and Statistical Science

I am a William W. Elliott Assistant Research Professor working on Analysis and PDE.

Contact Info:

Office Location:	06 Physics
Email Address:
Web Page:	http://www.math.duke.edu/~yuangao

Teaching (Spring 2021):

• MATH 212D.01D, MULTIVARIABLE CALCULUS Synopsis

  Online ON, WF 10:15 AM-11:05 AM

• MATH 212D.05D, MULTIVARIABLE CALCULUS Synopsis

  Online ON, WF 12:00 PM-12:50 PM

• MATH 712D.01D, MULTIVARIABLE CALCULUS Synopsis

  Online ON, WF 10:15 AM-11:05 AM

• MATH 712D.05D, MULTIVARIABLE CALCULUS Synopsis

  Online ON, WF 12:00 PM-12:50 PM

Office Hours:

Physics 06, TuTh 10am-11am and 2pm-3pm. Or by appointment.

Education:

Ph.D.

Fudan University (China)

2017

Research Interests: PDE, Calculus of Variation, Control Theory, Material Science

My research interest is the mathematical analysis of nonlinear evolution equations derived from physics problems, especially in materials science and surface science. I mainly work on 4th order degenerated parabolic equations, coupled equations with dynamic boundary condition and multiscale problems. The methods invovled are entropy method, calculus of variation, gradient flows, numerical simulation, operator theory, and control theory.

Keywords:

Diffusion processes and stochastic analysis on manifolds • Dimension reduction (Statistics) • General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems) • PDE in connection with control problems • PDE with multivalued right-hand sides • Simulation and numerical modeling

Recent Publications   (More Publications)   (search)

1. Gao, Y; Liu, JG, Large Time Behavior, Bi-Hamiltonian Structure, and Kinetic Formulation for a Complex Burgers Equation, Quarterly of Applied Mathematics, vol. 79 no. 1 (May, 2020), pp. 120-123, American Mathematical Society (AMS) [doi]  [abs]
2. Gao, Y; Liu, J-G, Long time behavior of dynamic solution to Peierls–Nabarro dislocation model, Methods and Applications of Analysis, vol. 27 no. 2 (2020), pp. 161-198, International Press of Boston [doi]
3. Gao, Y, Global strong solution with BV derivatives to singular solid-on-solid model with exponential nonlinearity, Journal of Differential Equations, vol. 267 no. 7 (September, 2019), pp. 4429-4447 [doi]  [abs]
4. Gao, Y; Liu, J-G; Lu, XY, Gradient flow approach to an exponential thin film equation: global existence and latent singularity, Esaim: Control, Optimisation and Calculus of Variations, vol. 25 (2019), pp. 49-49, E D P SCIENCES [doi]  [abs]
5. Gao, Y; Ji, H; Liu, JG; Witelski, TP, A vicinal surface model for epitaxial growth with logarithmic free energy, Discrete and Continuous Dynamical Systems Series B, vol. 23 no. 10 (December, 2018), pp. 4433-4453 [doi]  [abs]