Damião Júnio Araújo


Associate Professor
Department of Mathematics
Universidade Federal da Paraíba · UFPB
araujo@mat.ufpb.br

About


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.

Ice melting phenomenon
Image: NASA/Kathryn Hansen

Published and Accepted papers

Books


Submitted papers



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

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

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

  • On free boundary problems shaped by oscillatory singularities II: models in stochastic materials.
    (with G. Sá, E. Teixeira and J.M. Urbano)

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

  • On splitting complete manifolds via infinity harmonic functions.
    (with M. Magliaro, L. Mari and L. Pessoa)

  • Hausdorff measure estimates for the degenerate quenching problem.
    (with R. Teymurazyan and J.M. Urbano)

  • Interacting free boundaries in obstacle problems.
    (with R. Teymurazyan)

Teamwork



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.

Ice melting phenomenon
GS, Renato, DJA, AS, Rafael, Diego | July 2022.

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




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 (SBM Prize, 2023)
Current Position: Post-Doctorate Fellow at the University of Central Florida

Harish Shrivastava, Post-Doctorate | 2019
INCTMat CNPq fellowship