Asymptotic behavior of the Timoshenko-type system with nonlinear boundary control

2019 ◽  
Vol 10 (2) ◽  
pp. 171-182
Author(s):  
Mohamed Ali Ayadi ◽  
Ahmed Bchatnia
Keyword(s):  
Asymptotic Behavior ◽  
Wide Class ◽  
Existence And Uniqueness ◽  
Relaxation Function ◽  
Nonlinear Boundary ◽  
Type System ◽  
Timoshenko Type ◽  
Uniqueness Of The Solution ◽  
Boundary Dissipation ◽  
Nonlinear Boundary Control

AbstractIn this paper, we consider the Timoshenko-type system with nonlinear boundary dissipation. We prove the existence and uniqueness of the solution and we establish an explicit and general decay result for a wide class of the relaxation function, which depends on the length of the beam.

scholarly journals Safety Times for Multistage Assembly System

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Goran Lazovic ◽  
Vesna Sesum-Cavic ◽  
Slobodanka Mitrovic ◽  
Slobodan Radojevic ◽  
Nebojsa Dedovic ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Wide Class ◽  
Existence And Uniqueness ◽  
Assembly System ◽  
Exact Results ◽  
Holding Costs ◽  
One Stage ◽  
Uniqueness Of The Solution ◽  
Newsboy Model ◽  
Assembly Operations

Nowadays, a wide class of problems can be solved by using the classical newsboy model. However, in problems where uncertainty of events and randomness are omnipresent, there is a necessity to adapt the existing solutions and/or find new extensions that will properly answer all requirements. This paper considers a multistage assembly system where interrelated assembly operations with independent stochastic operation times should be planned in an optimal way. Delivery of items in a requested time implies that either delay costs or holding costs appear. The goal is to find optimal safety times. We propose an approximate technique based on successive application of the solution of simpler one-stage problem. The generalized mathematical model suggested is built up on the relaxed hypothesis and can be used in multistage assembly networks. The existence and uniqueness of the solution are proven. The preliminary tests are performed and our approximate technique is compared to exact results.

scholarly journals On the Harmonic Problem with Nonlinear Boundary Integral Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Saker Hacene
Keyword(s):  
Integral Equation ◽  
Existence And Uniqueness ◽  
Integral Method ◽  
Nonlinear Boundary ◽  
Monotone Operators ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Integral Conditions ◽  
Uniqueness Of The Solution ◽  
Harmonic Problem

In the present work, we deal with the harmonic problems in a bounded domain of ℝ2 with the nonlinear boundary integral conditions. After applying the Boundary integral method, a nonlinear boundary integral equation is obtained; the existence and uniqueness of the solution will be a consequence of applying theory of monotone operators.

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.

Stochastic elastic equation driven by multiplicative multi-parameter fractional noise

2017 ◽  
Vol 17 (02) ◽  
pp. 1750012 ◽  
Author(s):  
Yinghan Zhang ◽  
Xiaoyuan Yang
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Chaos Expansion ◽  
Distribution Space ◽  
Wiener Chaos ◽  
Fractional Noise ◽  
Undetermined Coefficient ◽  
Uniqueness Of The Solution ◽  
Wiener Chaos Expansion

In this paper, we consider the stochastic elastic equation driven by multiplicative multiparameter fractional noise. By using the Wiener chaos expansion and undetermined coefficient methods, we obtain the existence and uniqueness of the solution in a distribution space. The asymptotic behavior and the Hölder index of the solution are also estimated.

scholarly journals Fractional boundary value problems: Analysis and numerical methods

2011 ◽  
Vol 14 (4) ◽  
Author(s):  
Neville Ford ◽  
M. Morgado
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Of The Solution ◽  
Fractional Boundary Value Problems

AbstractIn this paper we consider nonlinear boundary value problems for differential equations of fractional order α, 0 < α < 1. We study the existence and uniqueness of the solution and extend existing published results. In the last part of the paper we study a class of prototype methods to determine their numerical solution.

scholarly journals Analysis of the Reynolds Equation for Lubrication in Case of Pressure-Dependent Viscosity

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Eduard Marušić-Paloka ◽  
Sanja Marušić
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Reynolds Equation ◽  
Homogenization Method ◽  
Nonlocal Effects ◽  
Pressure Dependent Viscosity ◽  
Uniqueness Of The Solution ◽  
Dependent Viscosity

We study the Reynolds equation, describing the ow of a lubricant, in case of pressure-dependent viscosity. First we prove the existence and uniqueness of the solution. Then, we study the asymptotic behavior of the solution in case of periodic roughness via homogenization method. Some interesting nonlocal effects appear due to the nonlinearity.

scholarly journals Two-scale homogenization of a stationary mean-field game

2020 ◽  
Vol 26 ◽  
pp. 17
Author(s):  
Rita Ferreira ◽  
Diogo Gomes ◽  
Xianjin Yang
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Mean Field ◽  
Main Tool ◽  
Homogenization Theory ◽  
Mean Field Game ◽  
First Order ◽  
Limit Problems ◽  
Uniqueness Of The Solution ◽  
Oscillating Potential

In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

scholarly journals Existence of Coupled Best Proximity Points of p-Cyclic Contractions

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Miroslav Hristov ◽  
Atanas Ilchev ◽  
Diana Nedelcheva ◽  
Boyan Zlatanov
Keyword(s):  
Wide Class ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Best Proximity Points ◽  
Cyclic Contractions ◽  
Ordered Pairs

We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate the results with an example that covers a wide class of maps.

scholarly journals New general decay result for a system of two singular nonlocal viscoelastic equations with general source terms and a wide class of relaxation functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Adel M. Al-Mahdi ◽  
Salim A. Messaoudi
Keyword(s):  
Wide Class ◽  
Relaxation Function ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
General Assumption ◽  
General Decay ◽  
Source Terms ◽  
Relaxation Functions ◽  
Viscoelastic Equations ◽  
General Source

Abstract This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function $k_{i}$ k i , namely, $$\begin{aligned} k_{i}^{\prime }(t)\le -\xi _{i}(t) \Psi _{i} \bigl(k_{i}(t)\bigr),\quad i=1,2. \end{aligned}$$ k i ′ ( t ) ≤ − ξ i ( t ) Ψ i ( k i ( t ) ) , i = 1 , 2 . We establish a new general decay result that improves most of the existing results in the literature related to this system. Our result allows for a wider class of relaxation functions, from which we can recover the exponential and polynomial rates when $k_{i}(s) = s^{p}$ k i ( s ) = s p and p covers the full admissible range $[1, 2)$ [ 1 , 2 ) .

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