We establish a Schauder-type estimate for general local and non-local linear parabolic
system $$\partial_tu+\mathbf {L} _su=\Lambda^\gamma f+ g $$ in $(0,\infty)\times\mathbb …

In this paper we prove the global existence, uniqueness, optimal large time decay rates, and
uniform gain of analyticity for the exponential PDE ht D eh in the whole space Rd x. We …

In this paper we study the existence assertion of the initial boundary value problem for the
equation ∂u∂t=Δe^-Δu. This problem arises in the mathematical description of the …

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 …

In the absence of external material deposition, crystal surfaces usually relax to become flat
by decreasing their free energy. We study analytically an asymmetry in the relaxation of …

A certain model for epitaxial film growth has recently attracted attention, with the existence of
small global solutions having been proved in both the case of the n‐dimensional torus and …

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 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 …