Author(s): Correia, Joaquim ; da Costa, Fernando ; Sirisack, Sackmone ; Vongsavang, Khankham
Date: 2020
Persistent ID: http://hdl.handle.net/10174/26615
Origin: Repositório Científico da Universidade de Évora
Subject(s): Burgers' equation; Method of characteristics; Cole-Hopf transformation; Traffic flow; Coagulation theory; Laplace transform
In this thesis, I present Burgers' equation and some of its applications. I consider the inviscid and the viscid Burgers' equations and present different analytical methods for their study: the Method of Characteristics for the inviscid case, and the Cole-Hopf Transformation for theviscid one. Two applications of Burgers' equations are given: one in simple models of Traffic Flow (which have been introduced independently by Lighthill-Whitham and Richards) and another in Coagulation theory (in which we use Laplace Transform to obtain Burgers' equations from the original coagulation integro-differential equation). In both applications we consider only analytical methods.
