Fábio Natali

Universidade Estadual de Maringá, Brazil

Title: On the orbital stability of periodic waves for some Klein-Gordon type equations

Abstract: The main purpose of this talk is to investigate the global well-posedness and orbital stability of odd periodic traveling waves for certain Klein-Gordon type equations in the Sobolev space of periodic functions with zero mean. We establish new results on the global well-posedness of weak solutions by combining a semigroup approach with energy estimates. As a consequence, we prove the orbital stability of odd periodic waves by applying a Morse index theorem to the constrained linearized operator defined in the Sobolev space with the zero mean property. In some particular cases, we also investigate the finite-time blow-up phenomena in the full energy space. This is joint work with Beatriz S. Lonardoni (UEM).