Boltzmann-type equations and their applications Ricardo Alonso Departamento de Matem´atica, PUC-Rio email: [email protected]Colombo/Americano Resumo Neste mini-curso cobriremos, em forma introdut´oria, alguns dos mais relevantes aspectos matem´aticos das equa¸ c˜oes de tipo Boltzmann e suas aplica¸c˜ oes a f´ ısica, economia e biologia. Construiremos a partir da teoria geral sobre gases ideais, ma- teriais granulados e propaga¸c˜ ao de onda, uma discuss˜ ao sobre alguns dos resultados matem´ aticos modernos de mais relevˆ ancia no ´area estudando suas provas. O mini- curso inclui material escrito com teoria, exemplos e discuss˜ao sobre problemas abertos parainvestiga¸c˜ ao. Pr´ e-requisitos Equa¸c˜ oes diferenciais parciais, teoria da medida e an´alise funcional de n´ ıvel inter- medi` ario. Abstract This mini-course will cover, in an introductory way, some of the most relevant math- ematical aspects of Boltzmann-type equations and their applications to physics, eco- nomics and biology. We will build up from the general theory on dilute gases, granu- lar materials and wave propagation a discussion of important modern mathematical results in the area sketching their proof. The mini-course includes written material with theory, examples and discussion of open problems and directions of research. Pre-Requisites Intermediate course of PDE’s, Measure Theory and Functional Analysis (advanced undergraduate or Master level). 1
Boltzmann-typeequationsandtheirapplicationsRicardoAlonsoDepartamentodeMatematica,PUC-Rioemail:
[email protected]/AmericanoResumoNeste mini-curso
cobriremos, emforma introdutoria, alguns dos mais
relevantesaspectos matematicos das equa coes detipoBoltzmannesuas
aplicac oes afsica,economiaebiologia.
Construiremosapartirdateoriageralsobregasesideais,
ma-teriaisgranuladosepropagac aodeonda,umadiscuss
aosobrealgunsdosresultadosmatem aticosmodernosdemaisrelev
ancianoareaestudandosuasprovas. Omini-curso inclui material escrito
com teoria, exemplos e discussao sobre problemas
abertosparainvestigac ao.Pre-requisitosEquac
oesdiferenciaisparciais, teoriadamedidaeanalisefuncional denvel
inter-medi` ario.AbstractThis mini-course will cover, in an
introductory way, some of the most relevant math-ematical aspects
of Boltzmann-type equations and their applications to physics,
eco-nomics and biology. We will build up from the general theory on
dilute gases, granu-lar materials and wave propagationa
discussionof important modern
mathematicalresultsintheareasketchingtheirproof.
Themini-courseincludeswrittenmaterialwiththeory,examplesanddiscussionofopenproblemsanddirectionsofresearch.Pre-RequisitesIntermediatecourseofPDEs,
MeasureTheoryandFunctional
Analysis(advancedundergraduateorMasterlevel).1
