Palestras e Seminários
auditório Luiz Antonio Favaro
Palestrante: Arnaldo Simal do Nascimento
Seminários de Equações Diferenciais

Resumo: Motivated by the study of nonlinear diffusion in surfaces we consider a scalar reaction-diffusion equation in a symmetric surface of revolution without boundary M not necessarily smooth at the plane of symmetry.

The aim is to understand how the geometry of the surface can give rise to stable/unstable nonconstant stationary solutions that will ultimately determine the dynamic of the gradient flow. This is fairly well-understood in the case that the two stable zeros of the bistable reaction term satisfies the so-called balanced condition which is not the case in this work.

The complete study of the asymptotic behavior of the one-parameter family of solutions is provided as it is the location of the transition layer as a function of the geometry of M as well as the other parameters.

Main tools are Gamma-convergence technique, for non-smooth functionals, and One-sided Calculus of Variations.


© 2018 Instituto de Ciências Matemáticas e de Computação