scholarly journals INVERSE PROBLEM FOR THE TIME-FRACTIONAL EULER-BERNOULLI BEAM EQUATION

2021 ◽  
Vol 26 (3) ◽  
pp. 503-518
Author(s):  
Ibrahim Tekin ◽  
He Yang
Keyword(s):  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Small Time ◽  
Beam Equation ◽  
Time Interval ◽  
Existence And Uniqueness Theorem ◽  
Bernoulli Beam ◽  
Additional Measurement ◽  
Small Time Interval ◽  
Euler Bernoulli Beam

In this paper, the classical Euler-Bernoulli beam equation is considered by utilizing fractional calculus. Such an equation is called the time-fractional EulerBernoulli beam equation. The problem of determining the time-dependent coefficient for the fractional Euler-Bernoulli beam equation with homogeneous boundary conditions and an additional measurement is considered, and the existence and uniqueness theorem of the solution is proved by means of the contraction principle on a sufficiently small time interval. Numerical experiments are also provided to verify the theoretical findings.

Solvability of coupled FBSDEs with diagonally quadratic generators

2017 ◽  
Vol 17 (06) ◽  
pp. 1750043 ◽  
Author(s):  
Peng Luo ◽  
Ludovic Tangpi
Keyword(s):  
Existence And Uniqueness ◽  
Small Time ◽  
Coupled Systems ◽  
Time Interval ◽  
Well Posedness ◽  
Initial Value ◽  
Small Time Interval ◽  
Uniqueness Of The Solution ◽  
Backward Sdes

We study the well-posedness for multi-dimensional and coupled systems of forward–backward SDEs when the generator can be separated into a quadratic and a subquadratic part. We obtain the existence and uniqueness of the solution on a small time interval. Moreover, the continuity and differentiability with respect to the initial value are presented.

Pointwise feedback stabilization of an Euler-Bernoulli beam in observations with time delay

2019 ◽  
Vol 25 ◽  
pp. 4 ◽  
Author(s):  
Kun-Yi Yang ◽  
Jun-Min Wang
Keyword(s):  
Time Delay ◽  
Open Loop ◽  
The State ◽  
Feedback Stabilization ◽  
Loop System ◽  
Beam Equation ◽  
Time Interval ◽  
Bernoulli Beam ◽  
Exponentially Stable ◽  
Euler Bernoulli Beam

This paper considers a one-dimensional Euler-Bernoulli beam equation where two collocated actuators/sensors are presented at the internal point with pointwise feedback shear force and angle velocity at the arbitrary position ξ in the bounded domain (0,1). The boundary x = 0 is simply supported and at the other boundary x = 1 there is a shear hinge end. Both of the observation signals are subjected to a given time delay τ ( >0). Well-posedness of the open-loop system is shown to illustrate availability of the observer. An observer is then designed to estimate the state at the time interval when the observation is available, while a predictor is designed to predict the state at the time interval when the observation is not available. Pointwise output feedback controllers are introduced to guarantee the closed-loop system to be exponentially stable for the smooth initial values when ξ ∈ (0, 1) is a rational number satisfying ξ ≠ 2l∕(2m − 1) for any integers l, m. Simulation results demonstrate that the proposed feedback design effectively stabilizes the performance of the pointwise control system with time delay.

scholarly journals The Problem of Determining of the Source Function and of the Leading Coefficient in the Many-dimensional Semilinear Parabolic Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 497-506
Author(s):  
Svetlana V. Polyntseva ◽  
◽  
Kira I. Spirina
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Source Function ◽  
Time Interval ◽  
Semilinear Parabolic Equation ◽  
Existence And Uniqueness Theorem ◽  
Bounded Functions ◽  
The Many ◽  
Semilinear Parabolic

We consider the problem of determining the source function and the leading coefficient in a multidimensional semilinear parabolic equation with overdetermination conditions given on two different hypersurfaces. The existence and uniqueness theorem for the classical solution of the inverse problem in the class of smooth bounded functions is proved. A condition is found for the dependence of the upper bound of the time interval, in which there is a unique solution to the inverse problem, on the input data

scholarly journals Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Ratchata Theinchai ◽  
Siriwan Chankan ◽  
Weera Yukunthorn
Keyword(s):  
Laplace Transform ◽  
Cantilever Beam ◽  
Adomian Decomposition Method ◽  
Small Deformation ◽  
Approximate Solutions ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Euler Bernoulli Beam

We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.

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