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Systems and partial differential equations

Grant number: 19/02512-5
Support type:Research Projects - Thematic Grants
Duration: September 01, 2019 - August 31, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Marcelo da Silva Montenegro
Grantee:Marcelo da Silva Montenegro
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Co-Principal Investigators:Ademir Pastor Ferreira ; Gabriela Del Valle Planas
Assoc. researchers:Alessio Fiscella ; Anne Caroline Bronzi ; Bianca Morelli Rodolfo Calsavara ; Djairo Guedes de Figueiredo ; Mahendra Prasad Panthee ; Marcelo Martins dos Santos ; Marcia Assumpcao Guimaraes Scialom
Associated grant(s):19/19491-0 - Solutions of higher-order models for water waves, AV.EXT

Abstract

The project consists of the study of central themes in partial differential equations and non-linear systems, both evolutionary and stationary. The main objective of our research are themathematical aspects of equations and systems that have great interaction with geometric pro-blems, reaction and diffusion models, phenomena in thermomechanics of continuous media andphysical-chemical behavior. We are interested in showing the existence of solutions and theirgeometric properties, regularity, uniqueness or not, stability or instability, formation of singula-rities or vortices, asymptotic behavior, approximation of solutions, well-posedeness, scatteringand dependence with respect to the initial data or any other important parameters that mayoccur in the problem. The mathematical techniques to be used rest on nonlinear analysis,variational methods, Schauder theory, approximation methods, subsolution and supersolutionmethod, Galerkin method, semigroup theory, Kato theory, among others. (AU)