## Research Interests for Yuan Gao

**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**
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- Dong, H; Gao, Y,
*Existence and uniqueness of bounded stable solutions to the Peierlsâ€“Nabarro model for curved dislocations*,
Calculus of Variations and Partial Differential Equations, vol. 60 no. 2
(April, 2021) [doi] [abs]
- Gao, Y; Lu, XY; Wang, C,
*Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects*,
Advances in Calculus of Variations
(January, 2021) [doi] [abs]
- Gao, Y; Liu, JG,
*Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface*,
Interfaces and Free Boundaries, vol. 23 no. 1
(January, 2021),
pp. 103-158 [doi] [abs]
- 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]
- Gao, Y; Liu, J-G,
*Long time behavior of dynamic solution to Peierlsâ€“Nabarro dislocation model*,
Methods and Applications of Analysis, vol. 27 no. 2
(2020),
pp. 161-198, International Press of Boston [doi]