Pullback attractors for nonautonomous difusion equations with delay

• Grant number: 18/02478-9
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2018
• End date: February 29, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Marcelo José Dias Nascimento
• Grantee: Izabella Durante Temporini Furtado
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The objective of this master's degree project is mainly focused on the study of non-autonomous parabolic partial differential equations. Let us consider semilinear partial differential equations, involving an unbounded operator (which explicitly depends on time $t$) that is an infinitesimal generator of an analytic semigroup. We will study the existence results of pullback attractor for the class of problems described above. Additionally, we intend to apply the abstract results to study the exponential decay of the solutions of non-autonomous diffusion equations with delay. (AU)