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- W2897795086 abstract "In this article, we prove the global (in time) existence of small data solutions from energy spaces basing on $L^q$ spaces, with $q in (1,infty)$, to the Cauchy problems for a weakly coupled system of semi-linear visco-elastic damped $sigma$-evolution models. Here we consider different power nonlinearities and different $sigma$ values in the comparison between two single equations. To do this, we use $(L^m cap L^q)- L^q$ and $L^q- L^q$ estimates, i.e., by mixing additional $L^m$ regularity for the data on the basis of $L^q- L^q$ estimates for solutions, with $m in [1,q)$, to the corresponding linear Cauchy problems. In addition, allowing loss of decay and the flexible choice of parameters $sigma$, $m$ and $q$ bring some benefits to relax the restrictions to the admissible exponents $p$." @default.
- W2897795086 created "2018-10-26" @default.
- W2897795086 creator A5021147517 @default.
- W2897795086 date "2018-10-21" @default.
- W2897795086 modified "2023-09-27" @default.
- W2897795086 title "A note on a weakly coupled system of semi-linear visco-elastic damped $sigma$-evolution models with different power nonlinearities and different $sigma$ values" @default.
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