Singular perturbation method for stability of infinite-dimensional systems.

RESUMEN: Coupled systems appear everywhere in complex models and in some cases there are different time scales involved. The coupling and the scales make this kind of system very difficult to study from theoretical and computational viewpoints. One hopes that some particular properties of the system could be studied through simpler uncoupled systems. This is what the singular perturbation method (SPM) does concerning stability properties. The SPM approach has been introduced for ordinary differential equations and can also be applied for partial differential equations but in the latter case there are no general theorems and stability properties have to be obtained for each particular system. In this talk we introduce the SPM for infinite-dimensional systems and obtain stability results. We will consider parabolic, hyperbolic and dispersive equations appearing in coupled systems in some cases also involving ordinary differential equations.

Posted on Sep 4, 2024 in Seminario IPCT, Seminars