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 …

A new approach to the construction of entropies and entropy productions for a large class of
nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of …

A fully discrete Lagrangian scheme for numerical solution of the nonlinear fourth-order
DLSS equation in one space dimension is analyzed. The discretization is based on the …

We propose a method for numerical integration of Wasserstein gradient flows based on the
classical minimizing movement scheme. In each time step, the discrete approximation is …

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 relaxation-time limit from the quantum hydrodynamic model to the quantum drift–
diffusion equations in R3 is shown for solutions which are small perturbations of the steady …

A logarithmic fourth-order parabolic equation in one space dimension with periodic
boundary conditions is studied. This equation arises in the context of fluctuations of a …

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 …

In this paper, an energy-stable finite element method with the Crank–Nicolson type of
temporal discretization scheme is developed and analyzed for a class of nonlinear fourth …