22 citations · 202 across the 36 of their papers we have counts for
19 papers · 1 filter
Phase-Field Models, Sharp Interface Limits, and Numerical Schemes for Contact Line Dynamics
Guosheng Fu, Yuan Gao, Jian-Guo Liu
We study phase-field and sharp-interface models for contact line dynamics of a liquid droplet on a solid substrate within a unified variational framework. The motion of the contact…
A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures
Yuan Gao, Jian-Guo Liu
This paper reinterprets Freidlin-Wentzell's variational construction of the rate function in the large deviation principle for invariant measures from the weak KAM perspective. Thr…
Large deviation principle and thermodynamic limit of chemical master equation via nonlinear semigroup
Yuan Gao, Jian-Guo Liu
Chemical reactions can be modeled by a random time-changed Poisson process on countable states. The macroscopic behaviors, such as large fluctuations, can be studied via the WKB re…
Asymptotic stability for diffusion with dynamic boundary reaction from Ginzburg-Landau energy
Yuan Gao, Jean-Michel Roquejoffre
The nonequilibrium process in dislocation dynamics and its relaxation to the metastable transition profile is crucial for understanding the plastic deformation caused by line defec…
Existence and rigidity of the Peierls-Nabarro model for dislocations in high dimensions
Yuan Gao, Jian-Guo Liu, Zibu Liu
We focus on existence and rigidity problems of the vectorial Peierls-Nabarro (PN) model for dislocations. Under the assumption that the misfit potential on the slip plane only depe…
Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects
Yuan Gao, Xin Yang Lu, Chong Wang
We study a nonlocal 4th order degenerate equation deriving from the epitaxial growth on crystalline materials. We first prove the global existence of evolution variational inequali…
Existence and uniqueness of bounded stable solutions to the Peierls-Nabarro model for curved dislocations
Hongjie Dong, Yuan Gao
We study the well-posedness of the vector-field Peierls-Nabarro model for curved dislocations with a double well potential and a bi-states limit at far field. Using the Dirichlet t…
Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates
Yuan Gao, Anya E. Katsevich, Jian-Guo Liu +2
We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and l…
Mathematical validation of the Peierls--Nabarro model for edge dislocations
Yuan Gao, Jian-Guo Liu, Tao Luo +1
In this paper, we perform mathematical validation of the Peierls--Nabarro (PN) models, which are multiscale models of dislocations that incorporate the detailed dislocation core st…
Long time behavior of dynamic solution to Peierls--Nabarro dislocation model
Yuan Gao, Jian-Guo Liu
In this paper we study the relaxation process of Peierls-Nabarro dislocation model, which is a gradient flow with singular nonlocal energy and double well potential describing how…
Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects
Yuan Gao, Jian-Guo Liu, Jianfeng Lu +1
We study a th order PDE with a nd order correction that is a modification of one suggested by Peter Smereka using the tools of Krug et al (Z. Phys. B., 1994). First, we provi…
Global Strong Solution With BV Derivatives to Singular Solid-on-Solid model With Exponential Nonlinearity
Yuan Gao
In this work, we consider the one dimensional very singular fourth-order equation for solid-on-solid model in attachment-detachment-limit regime with exponential nonlinearity $$h_t…
Large time behavior, bi-Hamiltonian structure and kinetic formulation for complex Burgers equation
Yu Gao, Yuan Gao, Jian-Guo Liu
We prove the existence and uniqueness of positive analytical solutions with positive initial data to the mean field equation (the Dyson equation) of the Dyson Brownian motion throu…
Gradient flow approach to an exponential thin film equation: global existence and latent singularity
Yuan Gao, Jian-Guo Liu, Xin Yang Lu
In this work, we study a fourth order exponential equation, derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow…
Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface
Yuan Gao, Jian-Guo Liu, Xin Yang Lu +1
In this work we consider which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the pr…
A vicinal surface model for epitaxial growth with logarithmic free energy
Yuan Gao, Hangjie Ji, Jian-Guo Liu +1
We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulti…
Global existence of solutions to a tear film model with locally elevated evaporation rates
Yuan Gao, Hangjie Ji, Jian-Guo Liu +1
Motivated by a model proposed by Peng et al. [Advances in Coll. and Interf. Sci. 206 (2014)] for break-up of tear films on human eyes, we study the dynamics of a generalized thin f…
Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime
Yuan Gao, Jian-Guo Liu, Jianfeng Lu
We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, , where , considered as a f…
Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces
Yuan Gao, Jian-Guo Liu, Jianfeng Lu
This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model following the work [Xiang, SIAM J. A…