A note on a weakly coupled system of semi-linear visco-elastic damped σ-evolution models with different power nonlinearities and different σ values

2018/10/21 by Dao, Tuan Anh
#35L30 #35L56 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.09664

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 ∈ (1,∞), to the Cauchy problems for a weakly coupled system of semi-linear visco-elastic damped σ-evolution models. Here we consider different power nonlinearities and different σ values in the comparison between two single equations. To do this, we use (L^m ∩ 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 ∈ [1,q), to the corresponding linear Cauchy problems. In addition, allowing loss of decay and the flexible choice of parameters σ, m and q bring some benefits to relax the restrictions to the admissible exponents p.

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