Determination of the initial condition in parabolic equations from boundary observations

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Dinh Nho Hào ◽  
Nguyen Thi Ngoc Oanh
Keyword(s):  
Variational Problem ◽  
Parabolic Equations ◽  
Numerical Scheme ◽  
Singular Values ◽  
Adjoint Problem ◽  
Splitting Methods ◽  
Initial Condition ◽  
Numerical Examples ◽  
Gradient Of The Functional

AbstractThe problem of determining the initial condition in parabolic equations from boundary observations is studied. It is reformulated as a variational problem and then a formula for the gradient of the functional to be minimized is derived via an adjoint problem. The variational problem is discretized by finite difference splitting methods and solved by the conjugate gradient method. Some numerical examples are presented to show the efficiency of the method. Also as a by-product of the variational method, we propose a numerical scheme for numerically estimating singular values of the solution operator in the inverse problem.

Space-time finite element method for determination of a source in parabolic equations from boundary observations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Phan Xuan Thanh
Keyword(s):  
Parabolic Equations ◽  
A Priori ◽  
Time Discretization ◽  
Adjoint Problem ◽  
Space Time ◽  
Dirichlet Data ◽  
Time Variables ◽  
Gradient Of The Functional ◽  
The Right

AbstractA novel inverse source problem concerning the determination of a term in the right-hand side of parabolic equations from boundary observation is investigated. The observation is given by an imprecise Dirichlet data on some part of the boundary. The unknown heat source is sought as a function depending on both space and time variables with an a priori information. The problem is reformulated as an optimal control problem with a Tikhonov regularization term. The gradient of the functional is derived via an adjoint problem. The space-time discretization approach is employed which allows the use of general space-time finite elements. The convergence of the approach is proved. Some numerical examples are presented for showing the efficiency of the approach.

Determination of the initial condition in parabolic equations from integral observations

2016 ◽  
Vol 25 (8) ◽  
pp. 1138-1167 ◽  
Author(s):  
Dinh Nho Hào ◽  
Nguyen Thi Ngoc Oanh
Keyword(s):  
Parabolic Equations ◽  
Initial Condition

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

scholarly journals Analysis of exponential splitting methods for inhomogeneous parabolic equations

2014 ◽  
Vol 35 (1) ◽  
pp. 161-178 ◽  
Author(s):  
E. Faou ◽  
A. Ostermann ◽  
K. Schratz
Keyword(s):  
Parabolic Equations ◽  
Splitting Methods ◽  
Exponential Splitting

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

Determination of Singularity-Free Zones in the Workspace of Planar 3-P̱RR Parallel Mechanisms

2006 ◽  
Vol 129 (6) ◽  
pp. 649-652 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanisms ◽  
Numerical Examples ◽  
Mathematical Derivation

This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3-P̱RR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach.

On the spectrum and the distribution of singular values of Schrödinger operators with a complex potential

1983 ◽  
Vol 388 (1794) ◽  
pp. 195-218 ◽  
Keyword(s):  
Complex Potential ◽  
Spectral Properties ◽  
Polynomial Growth ◽  
Schrödinger Operators ◽  
Singular Values ◽  
Negative Real Part ◽  
Adjoint Problem ◽  
Schrodinger Operators ◽  
Asymptotic Estimates ◽  
Integrability Conditions

This paper is concerned with spectral properties of the Schrödinger operator ─ ∆+ q with a complex potential q which has non-negative real part and satisfies weak integrability conditions. The problem is dealt with as a genuine non-self-adjoint problem, not as a perturbation of a self-adjoint one, and global and asymptotic estimates are obtained for the corresponding singular values. From these estimates information is obtained about the eigenvalues of the problem. By way of illustration, detailed calculations are given for an example in which the potential has at most polynomial growth.

Determination of source parameter in parabolic equations

Meccanica ◽  
1992 ◽  
Vol 27 (2) ◽  
pp. 85-94 ◽  
Author(s):  
J. R. Cannon ◽  
Yanping Lin ◽  
Shingmin Wang
Keyword(s):  
Parabolic Equations ◽  
Source Parameter
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