Bøger af Benoit Perthame

The thematic program Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications was held at the Institute for Mathematical Sciences at the National University of Singapore, from September 2019 to March 2020. Leading experts presented tutorials and special lectures geared towards the participating graduate students and junior researchers.Readers will find in this significant volume four expanded lecture notes with self-contained tutorials on modeling and simulation for collective dynamics including individual and population approaches for population dynamics in mathematical biology, collective behaviors for Lohe type aggregation models, mean-field particle swarm optimization, and consensus-based optimization and ensemble Kalman inversion for global optimization problems with constraints.This volume serves to inspire graduate students and researchers who will embark into original research work in kinetic models for collective dynamics and their applications.

This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations.

This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. The book further contains many original PDE problems originating in biosciences.