scholarly journals Asymptotic stability of porous-elastic system with thermoelasticity of type III

2021 ◽  
Author(s):  
Ilyes Lacheheb ◽  
Salim A. Messaoudi ◽  
Mostafa Zahri
Keyword(s):  
Wave Propagation ◽  
Asymptotic Stability ◽  
Finite Difference ◽  
Elastic System ◽  
Well Posedness ◽  
One Dimensional ◽  
Type Iii ◽  
The Stability ◽  
Theoretical Results ◽  
Finite Difference Techniques

AbstractIn this work, we investigate a one-dimensional porous-elastic system with thermoelasticity of type III. We establish the well-posedness and the stability of the system for the cases of equal and nonequal speeds of wave propagation. At the end, we use some numerical approximations based on finite difference techniques to validate the theoretical results.

scholarly journals On the Porous-Elastic System with Thermoelasticity of Type III and Distributed Delay: Well-Posedness and Stability

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Djamel Ouchenane ◽  
Abdelbaki Choucha ◽  
Mohamed Abdalla ◽  
Salah Mahmoud Boulaaras ◽  
Bahri Belkacem Cherif
Keyword(s):  
Lyapunov Functions ◽  
Elastic System ◽  
Distributed Delay ◽  
Mathematical Physics ◽  
Well Posedness ◽  
Engineering Structures ◽  
One Dimensional ◽  
Delay Term ◽  
Type Iii ◽  
The Stability

The paper deals with a one-dimensional porous-elastic system with thermoelasticity of type III and distributed delay term. This model is dealing with dynamics of engineering structures and nonclassical problems of mathematical physics. We establish the well posedness of the system, and by the energy method combined with Lyapunov functions, we discuss the stability of system for both cases of equal and nonequal speeds of wave propagation.

scholarly journals Well-posedness and energy decay of swelling porous elastic soils with a second sound and delay term

2021 ◽  
Author(s):  
Abdelli Manel ◽  
Lamine Bouzettouta ◽  
Guesmia Amar ◽  
Baibeche Sabah
Keyword(s):  
Wave Propagation ◽  
Delay Time ◽  
Elastic System ◽  
Semigroup Theory ◽  
Energy Decay ◽  
Well Posedness ◽  
Second Sound ◽  
One Dimensional ◽  
Delay Term

In this paper we consider a one-dimensional swelling porous-elastic system with second sound and delay term acting on the porous equation. Under suitable assumptions on the weight of delay, we establish the well-posedness of the system by using semigroup theory and we prove that the unique dissipation due to the delay time is strong enough to exponentially stabilize the system when the speeds of wave propagation are equal.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

Hybrid modeling of elastic‐wave propagation in two‐dimensional laterally inhomogeneous media

Geophysics ◽  
1987 ◽  
Vol 52 (6) ◽  
pp. 765-771 ◽  
Author(s):  
B. Kummer ◽  
A. Behle ◽  
F. Dorau
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Hybrid Scheme ◽  
Finite Difference Techniques

We have constructed a hybrid scheme for elastic‐wave propagation in two‐dimensional laterally inhomogeneous media. The algorithm is based on a combination of finite‐difference techniques and the boundary integral equation method. It involves a dedicated application of each of the two methods to specific domains of the model structure; finite‐difference techniques are applied to calculate a set of boundary values (wave field and stress field) in the vicinity of the heterogeneous domain. The continuation of the near‐field response is then calculated by means of the boundary integral equation method. In a numerical example, the hybrid method has been applied to calculate a plane‐wave response for an elastic lens embedded in a homogeneous environment. The example shows that the hybrid scheme enables more efficient modeling, with the same accuracy, than with pure finite‐difference calculations.

scholarly journals The effect of time-varying delay damping on the stability of porous elastic system

2021 ◽  
Vol 5 (1) ◽  
pp. 147-161
Author(s):  
Soh Edwin Mukiawa ◽  
Keyword(s):  
Elastic System ◽  
Time Varying ◽  
Viscoelastic System ◽  
One Dimensional ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

In the present work, we study the effect of time varying delay damping on the stability of a one-dimensional porous-viscoelastic system. We also illustrate our findings with some examples. The present work improve and generalize existing results in the literature.

An Analytical Study of Cryosurgery in the Lung

1992 ◽  
Vol 114 (4) ◽  
pp. 467-472 ◽  
Author(s):  
J. C. Bischof ◽  
J. Bastacky ◽  
B. Rubinsky
Keyword(s):  
Finite Difference ◽  
Analytical Study ◽  
Outer Boundary ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Thermal Phenomenon ◽  
Healthy Lung Tissue ◽  
Close Form ◽  
Finite Difference Techniques ◽  
Healthy Lung

The process of freezing in healthy lung tissue and in tumors in the lung during cryosurgery was modeled using one-dimensional close form techniques and finite difference techniques to determine the temperature profiles and the propagation of the freezing interface in the tissue. A thermal phenomenon was observed during freezing of lung tumors embedded in healthy tissue, (a) the freezing interface suddenly accelerates at the transition between the tumor and the healthy lung, (b) the frozen tumor temperature drops to low values once the freezing interface moves into the healthy lung, and (c) the outer boundary temperature has a point of sharp inflection corresponding to the time at which the tumor is completely frozen.

The Alekseev–Mikhailenko method applied to P–SV wave propagation in an elastic medium

1988 ◽  
Vol 25 (2) ◽  
pp. 226-234
Author(s):  
L. J. Pascoe ◽  
F. Hron ◽  
P. F. Daley
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Half Space ◽  
Elastic Half Space ◽  
Low Velocity ◽  
Seismic Modelling ◽  
Wave Propagation Problem ◽  
Modelling Techniques ◽  
Explicit Finite Difference ◽  
The Stability

The Alekseev–Mikhailenko method (AMM) is the name given to a series of algorithms that use one or more finite spatial transforms to reduce the dimensionality of a wave-propagation problem to that of one space dimension and time. This reduced equation is then solved using finite-difference techniques, and the space–time solution is recovered by applying inverse finite spatial transform(s). In this paper the elastodynamic wave equation that governs the coupled P–Sv motion in an isotropic, vertically inhomogeneous elastic half space is investigated using the AMM. Two types of impulsive body forces that may be used to excite the medium are examined, as is the problem of obtaining accurate transformed finite-difference analogues at the free surface. The second of these is accomplished by introducing the boundary conditions that the shear and normal stress must vanish here and by incorporating their transforms into the transformed elastodynamic equations. The stability criterion for the explicit finite-difference method is given cursory treatment, as detailed discussion of this aspect may be found in many texts that deal with the subject of finite differences.A coal-seam model (two thin, low-velocity layers embedded in a half space) illustrates the method. Both horizontal and vertical seismic traces are computed for this model and the results examined in relation to other seismic-modelling techniques.

Wave Propagation and Instability in a Circular Semi-Infinite Liquid Jet Harmonically Forced at the Nozzle

1978 ◽  
Vol 45 (3) ◽  
pp. 469-474 ◽  
Author(s):  
D. B. Bogy
Keyword(s):  
Wave Propagation ◽  
Radiation Condition ◽  
Liquid Jet ◽  
Propagation Characteristics ◽  
Frequency Spectra ◽  
One Dimensional ◽  
Wave Numbers ◽  
Complex Wave ◽  
The Stability ◽  
The Waves

The linearized form of the inviscid, one-dimensional Cosserat jet equations derived by Green [6] are used to study wave propagation in a circular jet with surface tension. The frequency spectra are shown for complex wave numbers for a complete range of Weber numbers. The propagation characteristics of the waves are studied in order to determine which branches of the frequency spectra to use in the semi-infinite jet problem with harmonic forcing at the nozzle. Two of the four branches are eliminated by a radiation condition that energy must be outgoing at infinity; the remaining two branches are used to satisfy the nozzle boundary conditions. The variation of the jet radius along its length is shown graphically for various Weber numbers and forcing frequencies. The stability or instability is explained in terms of the behavior of the two propagating phases.

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