Semilinear equations with absorption nonlinearities and measures as data

• Grant number: 24/05733-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: December 01, 2024
• End date: 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.