CA Ricardo Alonso Abs

Boltzmann-typeequationsandtheirapplicationsRicardoAlonsoDepartamentodeMatematica,PUC-Rioemail: ralonso@mat.puc-rio.brColombo/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