Báo cáo sinh học: " Research Article One-Dimensional Compressible Viscous Micropolar Fluid Model: Stabilization of the Solution for the Cauchy Problem" pot
... Problems
Volume 2010, Article ID 796065, 21 pages
doi:10.1155/2010/796065
Research Article
One-Dimensional Compressible Viscous
Micropolar Fluid Model: Stabilization of
the Solution for the Cauchy Problem
Nermina ... perturbations of the constants, we first
derive a priori estimates for the solution independent of T. In the second part of the w...
... Theory, Prentice-Hall, Upper Saddle
River, NJ, USA, 2002.
[15] G. Kitagawa, The two-filter formula for smoothing and an
implementation of the Gaussian-sum smoother,” Annals of the
Institute of ... is
available. Therefore, all the subsequent decisions in the frame
will be erroneous with high probability. The main feature
of the proposed algorithm is that the multimodali...
... to the types and the
density of log defects. The attenuation of X-ray in the logs
reduces the energy, reflected in different degrees of activating
the same image intensifier screen. The visual information
of ... cost function till
the convergence. Then, the result image was given by the
states of the neurons. The tools of Matlab were applied to
implement the...
... y)+ε. (3.12)
Then for each x
∈ X, there exists y ∈ Y such that g(x, y) >a,andforeachy ∈ Y,there
exist x
∈ X such that q(x, y) <b. Therefore, the conclusions (1) and (2) of Theorem 3.13
are ... consider the four set-valued mappings S
∗
,H
∗
,G
∗
,T
∗
: Y → 2
X
, then by the
same process of the proof of Case (1), we also conclude that there exists
x ∈ X such that
T(
x) = φ...
... either of i and
ii implies iv. Now, we show that iii implies iv. We notice that the set X
1
∩ X
2
is closed
by the closedness of S. Then, we need only to show that for any t ∈ R
1
,theset
A ... Assumption 1 hold, then f is l.s.c. function from
X
1
to R
1
∪{∞}. Further assume that the solution set X of VQVI is nonempty, then Domf
/
∅.
Proof. First we show that...
... α
t
α
.
3.30
From Theorem 3.1, we obtain the following corollary concerning the stability of 1.5 in
the sense of the JMRassias stability of functional equations controlled by the mixed product-
sum of powers ... of
Sciences of the United States of America, vol. 27, pp. 222–224, 1941.
8 T. Aoki, “On the stability of the linear transformation in Banach...
... s
q
σ
dσ ds.
3.24
The right-hand side of 3.24 tends to 0 as t
2
→ t
1
as a consequence of the continuity of St
in the uniform operator topology for t>0 by the compactness of St.SoI
3
→ ... 0.
3.27
So Φ is continuous.
By Krasnosel’skii’s theorem, we have the conclusion of the theorem.
Remark 3.3. In Theorem 3.2, if we furthermore suppose that the hyp...
... is the normal fundamental matrix of system 2.
By using the results developed in 5 for problems without impulses, the general
solution of the problem 1 bounded on the semiaxes has the form
x
t, ... dichotomous on the semiaxes
R
−
and R
and by using
the theory of pseudoinverse matrices, we establish necessary and sufficient conditions for the
indicated prob...
... determined. The procedure
describing the method of their deriving is a crucial part of the proof of Theorem 4.1 where we
give their form as well.
Proof. Substitute 4.18 into 4.3 and equate the terms ... coinciding
with the number of unknowns of a differential system with a single delay. As an example of
application of the results derived, the problem of bifurc...
... that x
∗
is a solution of the PBVP 1.1. Furthermore, we get from x
∗
∈ P
R
1
,R
2
that
δR
1
≤ δ
x
∗
≤ x
∗
t
≤
x
∗
≤ R
2
, for t ∈
0,σ
T
T
. 3.23
On the other hand, if ... fixed points of Φ are solutions of the PBVP 1.1.
Since ft, x is nondecreasing on x, we have the following lemma.
Advances in Difference Equations 3
Definition 2.6. For h>0, w...