Systems and partial differential equations

Abstract

The project consists of the study of central themes in partial differential equations and non-linear systems, both evolutionary and stationary. The main objective of our research are themathematical aspects of equations and systems that have great interaction with geometric pro-blems, reaction and diffusion models, phenomena in thermomechanics of continuous media andphysical-chemical behavior. We are interested in showing the existence of solutions and theirgeometric properties, regularity, uniqueness or not, stability or instability, formation of singula-rities or vortices, asymptotic behavior, approximation of solutions, well-posedeness, scatteringand dependence with respect to the initial data or any other important parameters that mayoccur in the problem. The mathematical techniques to be used rest on nonlinear analysis,variational methods, Schauder theory, approximation methods, subsolution and supersolutionmethod, Galerkin method, semigroup theory, Kato theory, among others. (AU)