22 citations · 202 across the 36 of their papers we have counts for
4 papers · 2 filters
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…