Theoretical Studies on the Inverse Problem in Electrocardiography and the Uniqueness of the Solution

1982 ◽  
Vol BME-29 (11) ◽  
pp. 719-725 ◽  
Author(s):  
Yasuo Yamashita
Keyword(s):  
Inverse Problem ◽  
Theoretical Studies ◽  
Uniqueness Of The Solution

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

scholarly journals Inverse problem for Sturm-Liouville operators on a curve

2019 ◽  
Vol 50 (3) ◽  
pp. 349-359
Author(s):  
Andrey Aleksandrovich Golubkov ◽  
Yulia Vladimirovna Kuryshova
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Transfer Matrix ◽  
Liouville Equation ◽  
Inverse Spectral Problem ◽  
Rectifiable Curve ◽  
Uniqueness Of The Solution ◽  
Sturm Liouville ◽  
Discontinuity Conditions ◽  
Liouville Operators

he inverse spectral problem for the Sturm-Liouville equation with a piecewise-entire potential function and the discontinuity conditions for solutions on a rectifiable curve \(\gamma \subset \textbf{C}\) by the transfer matrix along this curve is studied. By the method of a unit transfer matrix the uniqueness of the solution to this problem is proved with the help of studying of the asymptotic behavior of the solutions to the Sturm-Liouville equation for large values of the spectral parameter module.

scholarly journals On the existence and uniqueness of the solution of the coefficient inverse problem for a semilinear parabolic equation

2021 ◽  
Vol 2092 (1) ◽  
pp. 012008
Author(s):  
A L Sugezhik
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Source Function ◽  
Semilinear Parabolic Equation ◽  
Coefficient Inverse Problem ◽  
Uniqueness Of The Solution ◽  
Bounded Functions ◽  
Semilinear Parabolic

Abstract In this paper, we consider the problem of determining the source function and the coefficient by the derivative with respect to time in a semilinear parabolic equation with overdetermination conditions defined on two different hyperplanes. The existence and uniqueness theorems of the classical solution of the posed coefficient inverse problem in the class of smooth bounded functions were proved. An example of input data satisfying the conditions of the proved theorems is given.

Hemivariational inverse problem for contact problem with locking materials

2021 ◽  
Vol 8 (4) ◽  
pp. 665-677
Author(s):  
Z. Faiz ◽  
◽  
O. Baiz ◽  
H. Benaissa ◽  
D. El Moutawakil ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Contact Problem ◽  
Frictional Contact ◽  
Deformable Body ◽  
Lipschitz Mapping ◽  
Hemivariational Inequalities ◽  
Existence Of A Solution ◽  
Locally Lipschitz ◽  
Uniqueness Of The Solution ◽  
Dependence Result

The aim of this work is to study an inverse problem for a frictional contact model for locking material. The deformable body consists of electro-elastic-locking materials. Here, the locking character makes the solution belong to a convex set, the contact is presented in the form of multivalued normal compliance, and frictions are described with a sub-gradient of a locally Lipschitz mapping. We develop the variational formulation of the model by combining two hemivariational inequalities in a linked system. The existence and uniqueness of the solution are demonstrated utilizing recent conclusions from hemivariational inequalities theory and a fixed point argument. Finally, we provided a continuous dependence result and then we established the existence of a solution to an inverse problem for piezoelectric-locking material frictional contact problem.

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