The Cauchy problem for a class of hyperbolic operators

• Grant number: 09/13783-8
• Support Opportunities: Scholarships abroad - Research
• Start date: January 03, 2010
• End date: April 02, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Agreement: DAAD
• Principal Investigator: Marcelo Rempel Ebert
• Grantee: Marcelo Rempel Ebert
• Host Investigator: Michael Reissig
• Institution abroad: Technische Universität Bergakademie Freiberg (TU Bergakademie Freiberg), Germany
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In this project we are interested in discussing about necessary and sufficient conditions for the Cauchy problem so that a class ofweakly hyperbolic operators can be well-posed in spaces of functions like infinitely differentiable functions, Sobolev spaces or moreappropriate scales of function spaces. Because in the theory of weakly hyperbolic operators we have the effect of loss of regularity, we will study whether the loss of derivatives reallyappears and will determine upper and lower bounds for the loss of regularity. (AU)