Time: 9h30, Tuesday, October 13, 2020

Location: Room 302, Building A5, Institute of Mathematics

Abstract: In this talk, we study the following Cauchy problems for semi-linear damped sigma-evolution models with the power nonlinearities. We are interested in investigating L^1 estimates for oscillating integrals in the presentation of the solutions to the corresponding linear models with vanishing right-hand sides by applying the theory of modified Bessel functions combined with Faà di Bruno's formula and the Mikhlin-Hörmander multiplier theorem. By assuming additional L^m regularity on the initial data, we use (L^m cap L^q)- L^q and L^q- L^q estimates, with qin (1,infty) and min [1,q), to prove the global (in time) existence of small data Sobolev solutions to the semi-linear models from suitable function spaces basing on L^q spaces.