Damião Júnio Araújo

Associate Professor
Department of Mathematics
Universidade Federal da Paraíba · UFPB


team 2022  

I am currently based in João Pessoa - Paraíba - Brazil, in the Department of Mathematics at UFPB. 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. Image: NASA/Kathryn Hansen

Published and Accepted papers

Submitted papers

  • Fully nonlinear dead-core systems.
    (with R. Teymurazyan)

  • Sharp regularity for a singular fully nonlinear parabolic free boundary problem.
    (with G. Sá and J.M. Urbano)

  • Regularity in diffusion models with gradient activation.
    (with A. Sobral and E. Teixeira)

  • On free boundary problems with varying singularities.
    (with A. Sobral, E. Teixeira and J.M. Urbano)

  • On fractional quasilinear equations with elliptic degeneracy.
    (with D. dos Prazeres and E. Topp)

CV and others

Abridged CV

Currículo Lattes (In Portuguese)

Google Scholar



team 2022  

Aelson O. Sobral, Ph.D. student

Diego dos Santos, M.S. student

Renato de Andrade, Undergrad student

Felipe de Andrade, Undergrad student

Lucas Pontes, Undergrad student

Gustavo Gabriel Cunha, Highschool student

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.

Past students

Ginaldo S. Sá, Ph.D. student | 2023
Co-advised by José Miguel Urbano (KAUST - Saudi Arabia)
Thesis Publications: Calc. Var. Partial Differential Equations
Current Position: Post-Doctorate Fellow at the University of Central Florida

Harish Shrivastava, Post-Doctorate | 2019