Equations Differentielles a Points Singuliers Reguliers

Differential equations with "maxima"—differential equations that contain the maximum of the unknown function over a previous interval—adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval.

Authors: Sayas, Francisco-Javier
​Full description of the rudiments of the vector-valued distributions as needed for the theory of time domain integral equations
First detailed exposition of the mathematical techniques for boundary integral equations for the wave equation
Large collection of problems and exercises

This book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely many small particles. The mesoscopic equations are stochastic ordinary differential equations (SODEs) and stochastic partial differential equatuions (SPDEs), and the macroscopic limit is described by a parabolic partial differential equation.