We prove the global existence of non-negative variational solutions to the “drift diffusion”
evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under …

The logarithmic fourth-order equation \partial_tu+\frac12i,j=1^dij^2(uij^2\logu)=0, called the
Derrida–Lebowitz–Speer–Spohn equation, with periodic boundary conditions is analyzed …

Nonlinear diffusion equations of fourth and higher order have since long been of interest in
various fields of mathematical physics. Applications range from fluid models for thin viscous …

The goal of this paper is to give a non-local sufficient condition for generalized Poincaré
inequalities which extends the well-known Bakry-Emery condition. Such generalized …

A nonlinear fourth-order parabolic equation with nonhomogeneous Dirichlet–Neumann
boundary conditions in one space dimension is analyzed. This equation appears, for …

The quasineutral limit in the transient quantum drift-diffusion equations in one space
dimension is rigorously proved. The model consists of a fourth-order parabolic equation for …

The existence and semiclassical limit of the solution to one-dimensional transient quantum
drift-diffusion model in semiconductor simulation are discussed. Besides the proof of …

The global-in-time existence of weak nonnegative solutions to a sixth-order nonlinear
parabolic equation in one space dimension with periodic boundary conditions is proved …

In this paper we establish the orbital stability of periodic waves related to the logarithmic
Korteweg–de Vries equation. Our motivation is inspired in the recent work [3], in which the …

A logarithmic fourth-order parabolic equation in one space dimension with periodic
boundary conditions is analyzed. Using a new semidiscrete approximation in time, a first …