In this work, we study a fourth order exponential equation, ut= Δe− Δu derived from thin film
growth on crystal surface in multiple space dimensions. We use the gradient flow method in …

We study in this work a continuum model derived from a one-dimensional attachment-
detachment-limited type step flow on a vicinal surface, u_t=-u^2(u^3)_hhhh, where u …

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 …

The manufacturing of crystal films lies at the heart of modern nanotechnology. How to
accurately predict the motion of a crystal surface is of fundamental importance. Many …

In this paper we are concerned with the existence of a weak solution to the initial boundary
value problem for the equation ∂u∂t=Δ łeft (Δ u\right)^-3. This problem arises in the …

In this work we consider 1 w_t=\left\left (w_ hh+ c_0\right)^-3\right _ hh,\qquad w (0)= w^ 0,
wt= w hh+ c 0-3 hh, w (0)= w 0, which is derived from a thin film equation for epitaxial growth …

In this paper we study the boundary value problem for the equation div\left (D (∇ u) ∇\left
(div\left (| ∇ u|^ p-2 ∇ u+ β ∇ u| ∇ u|\right)\right)\right)+ au= f div D (∇ u)∇ div|∇ u| p-2∇ …

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 the …

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 resulting …

We study the continuum epitaxial model for elastic interacting atomic steps on vicinal
surfaces proposed by Xiang and E (Xiang, SIAM J. Appl. Math. 63: 241-258, 2002; Xiang …