| Grant number: | 19/15200-1 |
| Support Opportunities: | Regular Research Grants |
| Start date: | October 01, 2019 |
| End date: | September 30, 2021 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
| Principal Investigator: | Pedro Tavares Paes Lopes |
| Grantee: | Pedro Tavares Paes Lopes |
| Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| City of the host institution: | São Paulo |
Abstract
We propose to study problems involving evolution equations, where pseudodifferential operators appear as useful tools or have a close connection to. We intend to study the resolvent and the holomorphic functional calculus of pseudodifferential operators on manifolds with conical singularities, having in mind applications to linear and nonlinear parabolic equations. In particular, we would like to prove the existence of a H infinity calculus for these operators. We will also continue to explore the concrete problems that we have studied in the last years: the Cahn-Hilliard equation, particularly on manifolds with conical singularities, and the problems with dynamic boundary conditions. The latter problem can, under certain circumstances, be rewritten as a pseudodifferential parabolic equation on a surface. In the concrete applications, we would like to explore specially the dynamic behavior of the solutions of the equations, using, eventually, results obtained with pseudodifferential operators. (AU)
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