Global existence for weakly coupled systems of semi-linear structurally damped σ-evolution models with different power nonlinearities

2018/09/17 by Dao, Tuan Anh
#35L30 #35L56 #35S05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.06744

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 L^m regularity on the initial data, with m ∈ [1,2), we use (L^m ∩ L²)- L² and L²- L² 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.

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