scholarly journals Dispersion Bound for the Wyner-Ahlswede-Körner Network via a Semigroup Method on Types

2020 ◽  
pp. 1-1
Author(s):  
Jingbo Liu
Keyword(s):  
Semigroup Method

A stability result of a Timoshenko system in thermoelasticity of second sound with a delay term in the internal feedback

2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Djamel Ouchenane
Keyword(s):  
Heat Conduction ◽  
Stability Result ◽  
Well Posedness ◽  
Second Sound ◽  
Timoshenko System ◽  
Wave Speeds ◽  
One Dimensional ◽  
Delay Term ◽  
Semigroup Method ◽  
Cattaneo’S Law

AbstractIn this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay term in the feedback. The heat conduction is given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem. Furthermore, an exponential stability result is shown without the usual assumption on the wave speeds. To achieve our goals, we make use of the semigroup method and the energy method.

Singular first order perturbations of the heat equation

1984 ◽  
Vol 96 (3-4) ◽  
pp. 317-321
Author(s):  
Joel Avrin
Keyword(s):  
Heat Equation ◽  
Magnetic Vector ◽  
First Order ◽  
Vector Potentials ◽  
Semigroup Method

SynopsisWe exhibit dimension-independent conditions under which the formal operator A = −Δ + a.∇ + V can be defined on such that its closure Ā in L2(Rs, dx) is quasi-m-accretive. Here, a is real so that Ā is nonselfadjoint. the method of proof is a generalized version of the argument employed in the portion of the author's thesis where term a.∇ was originally considered. Specifically, we construct exp (−tĀ) as a limit of approximating semigroups. Since the thesis appeared, Kato has also dealt with the term a. ∇ his conditions on a and V are similar to, but more general than, the conditions that appear here; in addition, he considers magnetic vector potentials. Of interest here is the semigroup method itself, the conciseness of the arguments thereby produced, and a relaxed condition on div a.

Polynomial Stability for Timoshenko-Type System with Past History

2014 ◽  
Vol 623 ◽  
pp. 78-84
Author(s):  
Zhi Yong Ma
Keyword(s):  
Relaxation Function ◽  
Wave Speed ◽  
Past History ◽  
Type System ◽  
Stability Result ◽  
Equation Modeling ◽  
Polynomial Stability ◽  
Timoshenko Type ◽  
Semigroup Method ◽  
Vibrating Systems

In this paper, we consider hyperbolic Timoshenko-type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. We use semigroup method to prove the polynomial stability result with assumptions on past history relaxation function exponentially decaying for the nonequal wave-speed case.

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