Grant number: 19/27717-9 Support type: Scholarships in Brazil - Master Effective date (Start): July 01, 2020 Effective date (End): February 28, 2022 Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis Principal researcher: Marcelo José Dias Nascimento Grantee: Vitória Soares dos Santos Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil Abstract The main of this master's degree project is to study of non-autonomous parabolic/hyperbolic partial differential equations. We will study the notion of time-dependent attractor for process $U(t,\tau): X_{\tau} \to X_{t}$ exploiting the minimality with respect to the pullback attraction property. Finally, we will applied the abstract results to study the longterm behavior of wave equations with time- dependent speed of propagation. (AU)