Affiliation:
1. Faculty of Mathematics and Informatics , [ 118018]Hanoi University of Science and Technology, No. 1 Dai Co Viet road , Hanoi , Vietnam
2. Laboratory of Analysis and Control of PDEs , [ 124749]Djillali Liabes University, P. O.Box 89 , Sidi Bel Abbes 22000 , Algeria
Abstract
Abstract
In this paper, we are interested in studying the Cauchy problem for a weakly coupled system of two semi-linear structurally damped
σ
k
{\sigma_{k}}
-evolution equations, where
σ
k
≥
1
{\sigma_{k}\geq 1}
for
k
=
1
,
2
{k=1,2}
. Our first purpose involves the proof of global (in time) existence of small data energy solutions by mixing additional
L
m
k
{L^{m_{k}}}
regularity for the data, where
m
k
∈
[
1
,
2
)
{m_{k}\in[1,2)}
. We want to point out that in some cases of choosing suitable parameters
m
k
{m_{k}}
, with
k
=
1
,
2
{k=1,2}
, the obtained lower bound of one exponent p or q related to power nonlinearities on the right-hand sides is really smaller than the critical exponent, the so-called modified Fujita exponent. The second aim of this paper is to discuss a blow-up result for Sobolev solutions with any different fractional values of
σ
k
≥
1
{\sigma_{k}\geq 1}
when
m
1
=
m
2
{m_{1}=m_{2}}
.
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