Global existence of solutions for weakly coupled systems of semi-linear structurally damped σ-evolution models

Abstract

ABSTRACT In this paper, we study the Cauchy problems for weakly coupled systems of semi-linear structurally damped σ-evolution models with different power nonlinearities. By assuming additional regularity on the initial data, with , we use and estimates for solutions to the corresponding linear Cauchy problems to prove the global (in time) existence of small data Sobolev solutions to the weakly coupled systems of semi-linear models from suitable function spaces for any and . Moreover, not only the nonexistence of global solution is indicated by using test function method, but also a lifespan estimate is discussed when σ and are integers.