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 …

In this paper we study the large time behavior of the solutions to the following nonlinear
fourth-order equations $$\partial_t u=\Delta e^{-\Delta u}, $$$$\partial_t u=-u^ 2\Delta^ 2 (u …

We study a 4th order degenerate parabolic PDE model in one-dimension with a 2nd order
correction modeling the evolution of a crystal surface under the influence of both thermal …

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 aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-
elliptic system arising from biological transport networks. For such problem, we first establish …

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 …

We consider a spatially homogeneous Kolmogorov–Vicsek model in two dimensions, which
describes the alignment dynamics of self-driven stochastic particles that move on a plane at …

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 paper we prove the global existence of a strong solution to the initial boundary value
problem for the exponential partial differential equation∂ tu− Δ e− Δ u+ e− Δ u− 1= 0. 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 …