In the manuscript, we are interested in using kinetic theory to better understand the time
evolution of wealth distribution and their large scale behavior such as the evolution of …

A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction
of a model from quantum statistical mechanics and also as the gradient flow of a second …

This paper is concerned with the analysis of a sixth-order nonlinear parabolic equation
whose solutions describe the evolution of the particle density in a quantum fluid. We prove …

The mechanisms behind the emergence of collective behaviors arising from physics,
biology, economics and many other related fields have drawn a lot of attention among the …

We present an algorithm for the derivation of lower bounds on support propagation for a
certain class of nonlinear parabolic equations. We proceed by combining the ideas in some …

1A. The equation. The following nonlinear parabolic evolution equation of sixth order is
considered:∂ tu= div (u∇((u)+ λ3| x| 2)),(u)= 1 2∇ 2 logu2+ 1 u∇ 2:(u∇ 2 logu),(1) where …

In this paper, we study the entropy estimates of radially symmetric solutions to a fourth order
nonlinear degenerate problem related to image processing in higher dimensions. The …

Conservation laws and dissipated quantities are fundamental in analysis. Here we discuss
them in partial differential equations and their discretizations. These quantities are integral …

The main aim of this paper is to give some theoretical analysis for a nonlinear higher order
total variation image model. Applying the algebraic approach, we transform the analytical …

The computation of the second time derivative of the entropy in Chap. 2 involves a number
of smartly chosen integrations by parts. In this chapter, we show that these calculations can …