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.
Acknowledgments
The author would like to express sincere thankfulness to Professor Michael Reissig for his many helpful suggestions and Institute of Applied Analysis for their hospitality. The author wishes to thank the referee for his careful reading of the manuscript and for valuable comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).