The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

This book gives an exposition of the principal concepts and results related to second order
elliptic and parabolic equations for measures, the main examples of which are Fokker …

The description of emerging collective phenomena and self-organization in systems
composed of large numbers of individuals has gained increasing interest from various …

The Heat Equation is one of the three classical linear partial differential equations of second
order that form the basis of any elementary introduction to the area of PDEs, and only …

This book presents models written as partial differential equations and originating from
various questions in population biology, such as physiologically structured equations …

Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book
discusses fundamental properties of transient and stationary solutions, emphasizing the …

The long-time asymptotics of certain nonlinear, nonlocal, diffusive equations with a gradient
flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and …

We consider the attraction–repulsion chemotaxis system under homogeneous Neumann
boundary conditions in a bounded domain Ω⊂ ℝn with smooth boundary, where χ≥ 0, ξ≥ …

This text is concerned with the quantitative aspects of the theory of nonlinear diffusion
equations; equations which can be seen as nonlinear variations of the classical heat …

The global-in-time existence of bounded weak solutions to a large class of physically
relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is …