Scholarship 24/05733-0 - Equações diferenciais parciais - BV FAPESP
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Semilinear equations with absorption nonlinearities and measures as data

Grant number: 24/05733-0
Support Opportunities:Scholarships in Brazil - Master
Start date until: December 01, 2024
End date until: February 28, 2026
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Adilson Eduardo Presoto
Grantee:Carlos Eduardo Passarin Segantin
Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Associated research grant:22/16407-1 - TESdE: Thematic on Equations and Systems of differential Equations, AP.TEM

Abstract

Since their origins the development of Partial Differential Equations has gone hand in hand with progress in Physics; it has been particulary influenced by the Relativistic Physics. The introduction of adequate tools to deal with the emergent questions were provided by Functional Analysis and the Theories of Measures and the Distributions. Having new function spaces and more powerful results at hand, the hope to solve PDEs has greatly expanded and flourished the area.Stating physical problems based on quantum mechanical premisses led to new models in Differential Equations which require data with weaker integrability conditions like \(L^1\)-integrability or just being a measure. Examples are the Thomas-Fermi equations or the Chern-Simon system with Higgs particles. In this work, we will investigate elliptic semilinear equations with nonlinearity of absorption type, passing from Poisson's equations to nonlinear equations, always having measures as data.

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