scholarly journals Boundary Stabilization of Memory Type for the Porous-Thermo-Elasticity System

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Abdelaziz Soufyane ◽  
Mounir Afilal ◽  
Mama Chacha
Keyword(s):  
Elastic System ◽  
Decay Rates ◽  
General Decay ◽  
Polynomial Decay ◽  
Boundary Stabilization ◽  
One Dimensional ◽  
Elasticity System ◽  
Special Cases ◽  
Memory Type ◽  
The One

We consider the one-dimensional viscoelastic Porous-Thermo-Elastic system. We establish a general decay results. The usual exponential and polynomial decay rates are only special cases.

scholarly journals General decay of solutions of a thermoelastic Bresse system with viscoelastic boundary conditions

2021 ◽  
Vol 39 (6) ◽  
pp. 157-182
Author(s):  
Ammar Khemmoudj
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Decay Rates ◽  
General Decay ◽  
Polynomial Decay ◽  
Relaxation Functions ◽  
Bresse System ◽  
Decay Of Solutions ◽  
Special Cases

In this paper we consider a multidimensional thermoviscoelastic system of Bresse type where the heat conduction is given by Green and Naghdi theories. For a wider class of relaxation functions, We show that the dissipation produced by the memory eect is strong enough to produce a general decay results. We establish a general decay results, from which the usual exponential and polynomial decay rates are only special cases.

Polynomial stability for the equations of porous elasticity in one-dimensional bounded domains

2021 ◽  
pp. 108128652110190
Author(s):  
D. S. Almeida Júnior ◽  
A. J. A. Ramos ◽  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
T. El Arwadi
Keyword(s):  
Elastic System ◽  
Polynomial Decay ◽  
Bounded Domains ◽  
Porous Structures ◽  
Polynomial Stability ◽  
One Dimensional ◽  
The One

In this paper, we consider a porous–elastic system where the dissipation mechanisms act on the elastic and on the porous structures. Here, we consider the one-dimensional porous–elastic system defined on bounded domains in space and we proved the polynomial stability when a particular relationship between the damping parameters is equal to zero. We also prove the optimality of the rate of polynomial decay.

scholarly journals General Decay for the Degenerate Equation with a Memory Condition at the Boundary

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Su-Young Shin ◽  
Jum-Ran Kang
Keyword(s):  
Decay Rates ◽  
General Decay ◽  
Polynomial Decay ◽  
Degenerate Equation ◽  
Memory Condition ◽  
Relaxation Functions ◽  
Special Cases

We consider a degenerate equation with a memory condition at the boundary. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.

The general Lie group and similarity solutions for the one-dimensional Vlasov–Maxwell equations

1985 ◽  
Vol 33 (2) ◽  
pp. 219-236 ◽  
Author(s):  
Dana Roberts
Keyword(s):  
Lie Group ◽  
Maxwell Equations ◽  
Transformation Group ◽  
Spatial Dimension ◽  
Similarity Solutions ◽  
One Dimensional ◽  
Special Cases ◽  
General Similarity ◽  
The One ◽  
The Individual

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov–Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multi-species case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution (t→∞) for a one-species, one-dimensional plasma is one of the general similarity solutions.

Moments of the first-passage time of a Wiener process with drift between two elastic barriers

1995 ◽  
Vol 32 (4) ◽  
pp. 1007-1013 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Wiener Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Special Cases ◽  
Backward Equation ◽  
The One ◽  
First Passage Problem ◽  
Reflecting Barriers

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

scholarly journals Optimal Polynomial Decay to Coupled Wave Equations and Its Numerical Properties

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
R. F. C. Lobato ◽  
S. M. S. Cordeiro ◽  
M. L. Santos ◽  
D. S. Almeida Júnior
Keyword(s):  
Decay Rate ◽  
Spectral Methods ◽  
Finite Differences ◽  
Wave Equations ◽  
Coupled System ◽  
Polynomial Decay ◽  
One Dimensional ◽  
Coupled Wave Equations ◽  
Optimal Polynomial ◽  
The One

In this work we consider a coupled system of two weakly dissipative wave equations. We show that the solution of this system decays polynomially and the decay rate is optimal. Computational experiments are conducted in the one-dimensional case in order to show that the energies properties are preserved. In particular, we use finite differences and also spectral methods.

scholarly journals Applications of (a,b)-continued fraction transformations

2011 ◽  
Vol 32 (2) ◽  
pp. 739-761 ◽  
Author(s):  
SVETLANA KATOK ◽  
ILIE UGARCOVICI
Keyword(s):  
Continued Fraction ◽  
Natural Extension ◽  
Absolutely Continuous ◽  
Coding Sequences ◽  
One Dimensional ◽  
Sofic Shift ◽  
Absolutely Continuous Invariant Measure ◽  
Special Cases ◽  
The One ◽  
Absolutely Continuous Invariant

AbstractWe describe a general method of arithmetic coding of geodesics on the modular surface based on the study of one-dimensional Gauss-like maps associated to a two-parameter family of continued fractions introduced in [Katok and Ugarcovici. Structure of attractors for (a,b)-continued fraction transformations.J. Modern Dynamics4(2010), 637–691]. The finite rectangular structure of the attractors of the natural extension maps and the corresponding ‘reduction theory’ play an essential role. In special cases, when an (a,b)-expansion admits a so-called ‘dual’, the coding sequences are obtained by juxtaposition of the boundary expansions of the fixed points, and the set of coding sequences is a countable sofic shift. We also prove that the natural extension maps are Bernoulli shifts and compute the density of the absolutely continuous invariant measure and the measure-theoretic entropy of the one-dimensional map.

Lattice Animals and Self-Organized Criticality

Fractals ◽  
1997 ◽  
Vol 05 (02) ◽  
pp. 199-213 ◽  
Author(s):  
A. Yu Shahverdian
Keyword(s):  
Weyl’S Theorem ◽  
Dynamical System Theory ◽  
Lattice Animals ◽  
Additional Time ◽  
One Dimensional ◽  
Self Organized ◽  
Special Cases ◽  
Self Organized Criticality ◽  
The One

The paper considers one model of SOC close to BTW and slider blocks models. In addition, it introduces an additional time parameter and imposes special restrictions on the avalanche geometrical structure. The generalization and modification of the avalanche's concept allows us to apply H. Weyl's theorem in the dynamical system theory so as to obtain the strong and exact results in this area. We introduce some combinatorial characteristic of clusters and use it as a tool for estimating the frequency of the avalanches. The results obtained give the asymptotically exact expressions for the asymptotical frequency as well as two special types of such extended avalanches. In some special cases, they reduce the determination of the frequency of the avalanches to combinatorial enumerative problem for lattice animals on the d-dimensional torus. The other two results are related to the one-dimensional model and establish the connection between the SOC and the theory of number partitions.

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