Associate Professor
Department of Mathematics
Universidade Federal da Paraíba · UFPB
araujo@mat.ufpb.br
I am currently based in the vibrant city of João Pessoa, state of Paraíba, Brazil, in the Department of Mathematics at the Universidade Federal da Paraíba. I am conducting research into geometric and analytical techniques for partial differential equations and free boundary problems. Our aim is to provide precise regularity (smoothness) estimates of solutions to these problems. Regularity is crucial for numerical computations, and a lack of smoothness can describe how wild the behavior of models are. Of particular interest are my recent works on problems involving degenerate PDEs, in which the diffusion properties of governing operators degenerate along free boundaries - a priori unknown sets. One notable example is the phenomenon of ice melting into water, where the free boundary refers to the interface between water and ice, namely, the solid-liquid interface. Such mathematical scenarios are also related to jet and cavitational flows, gas and liquid flows in porous media, and financial mathematics, among others.
We warmly invite students of all levels and disciplines related to mathematics to reach out to us regarding research projects centered around introductory topics in the analysis of differential equations, functional analysis, and measure theory, whether you are an undergraduate, master's, or Ph.D. We strongly encourage girls to join our research group, as we are committed to promoting inclusivity and gender equality in scientific research.
Aelson O. Sobral, Ph.D. student
Diego dos Santos, Ph.D. student
Aureliana Tavares, M.S. student
Renato de Andrade, Undergrad student
Felipe de Andrade, Undergrad student
Lucas Pontes, Undergrad student
José Ygor Leal, Highschool student
Marlisson dos Santos, Highschool student
Ginaldo S. Sá, Ph.D. student | 2023
Co-advised by José Miguel Urbano (KAUST - Saudi Arabia)
Thesis Publications: Calc. Var. Partial Differential Equations (SBM Prize, 2023)
Current Position: Post-Doctorate Fellow at the University of Central Florida
Harish Shrivastava, Post-Doctorate | 2019
INCTMat CNPq fellowship