Stochastic processes and applications
GA Pavliotis - Texts in applied mathematics, 2014 - Springer
The purpose of this book is to present various results and techniques from the theory of
stochastic processes and in particular diffusion processes that are useful in the study of …
stochastic processes and in particular diffusion processes that are useful in the study of …
[BOOK][B] Interacting multiagent systems: kinetic equations and Monte Carlo methods
L Pareschi, G Toscani - 2013 - books.google.com
The description of emerging collective phenomena and self-organization in systems
composed of large numbers of individuals has gained increasing interest from various …
composed of large numbers of individuals has gained increasing interest from various …
[PDF][PDF] Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions.
The Keller-Segel system describes the collective motion of cells which are attracted by a
chemical substance and are able to emit it. In its simplest form it is a conservative drift …
chemical substance and are able to emit it. In its simplest form it is a conservative drift …
[HTML][HTML] Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids
Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute
gases of uncharged noninteracting point particles described in elementary textbooks …
gases of uncharged noninteracting point particles described in elementary textbooks …
Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2
We analyze the two‐dimensional parabolic‐elliptic Patlak‐Keller‐Segel model in the whole
Euclidean space ℝ2. Under the hypotheses of integrable initial data with finite second …
Euclidean space ℝ2. Under the hypotheses of integrable initial data with finite second …
General relative entropy inequality: an illustration on growth models
P Michel, S Mischler, B Perthame - Journal de mathématiques pures et …, 2005 - Elsevier
We introduce the notion of General Relative Entropy Inequality for several linear PDEs. This
concept extends to equations that are not conservation laws, the notion of relative entropy …
concept extends to equations that are not conservation laws, the notion of relative entropy …
A result on parabolic gradient regularity in Orlicz spaces and application to absorption-induced blow-up prevention in a Keller–Segel-type cross-diffusion system
M Winkler - International Mathematics Research Notices, 2023 - academic.oup.com
Abstract The Neumann problem for (0.1) is considered in bounded domains with smooth
boundary, where and. By means of a variational approach, a statement on boundedness of …
boundary, where and. By means of a variational approach, a statement on boundedness of …
Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method
The purpose of this work is to establish a quantitative and constructive stability result for a
class of subcritical Gagliardo-Nirenberg-Sobolev inequalities which interpolates between …
class of subcritical Gagliardo-Nirenberg-Sobolev inequalities which interpolates between …
Variational bounds and nonlinear stability of an active nematic suspension
S Weady - Journal of Fluid Mechanics, 2024 - cambridge.org
We use the entropy method to analyse the nonlinear dynamics and stability of a continuum
kinetic model of an active nematic suspension. From the time evolution of the relative …
kinetic model of an active nematic suspension. From the time evolution of the relative …
Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast
diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt …
diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt …