scholarly journals Analysis of direct and inverse problems for a fractional elastoplasticity model

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 699-708 ◽  
Author(s):  
Salih Tatar ◽  
Süleyman Ulusoy
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Unique Solution ◽  
Continuous Dependence ◽  
Direct Problem ◽  
Direct And Inverse Problems

This study is devoted to a nonlinear time fractional inverse coeficient problem. The unknown coeffecient depends on the gradient of the solution and belongs to a set of admissible coeffecients. First we prove that the direct problem has a unique solution. Afterwards we show the continuous dependence of the solution of the corresponding direct problem on the coeffecient, the existence of a quasi-solution of the inverse problem is obtained in the appropriate class of admissible coeffecients.

scholarly journals Inverse Problems for Degenerate Fractional Integro-Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 532
Author(s):  
Mohammed Al Horani ◽  
Mauro Fabrizio ◽  
Angelo Favini ◽  
Hiroki Tanabe
Keyword(s):  
Inverse Problem ◽  
Partial Differential Equations ◽  
Inverse Problems ◽  
Differential Equations ◽  
Banach Spaces ◽  
Unique Solution ◽  
Direct Problem ◽  
Regularity Of Solutions ◽  
Strict Solution ◽  
Fractional Equations

This paper deals with inverse problems related to degenerate fractional integro-differential equations in Banach spaces. We study existence, uniqueness and regularity of solutions to the problem, claiming to extend well known studies for the case of non-fractional equations. Our method is based on transforming the inverse problem to a direct problem and identifying the conditions under which this direct problem has a unique solution. The conditions under which the unique strict solution can be compared with the case of a mild solution, obtained in previous studies under quite restrictive requirements, are on the underlying functions. Applications from partial differential equations are given to illustrate our abstract results.

NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 106-110
Author(s):  
S.E. Kasenov ◽  
◽  
G.E. Kasenova ◽  
A.A. Sultangazin ◽  
B.D. Bakytbekova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
Direct Problem ◽  
Nonlinear Differential Equations ◽  
Direct And Inverse Problems ◽  
Additional Information ◽  
Several Variables ◽  
Gradient Of The Functional ◽  
Objective Functional

The article considers direct and inverse problems of a system of nonlinear differential equations. Such problems are often found in various fields of science, especially in medicine, chemistry and economics. One of the main methods for solving nonlinear differential equations is the numerical method. The initial direct problem is solved by the Rune-Kutta method with second accuracy and graphs of the numerical solution are shown. The inverse problem of finding the coefficients of a system of nonlinear differential equations with additional information on solving the direct problem is posed. The numerical solution of this inverse problem is reduced to minimizing the objective functional. One of the methods that is applicable to nonsmooth and noisy functionals, unconditional optimization of the functional of several variables, which does not use the gradient of the functional, is the Nelder-Mead method. The article presents the NellerMead algorithm. And also a numerical solution of the inverse problem is shown.

scholarly journals Mathematical models of centers of equal pressure in stellar systems

2021 ◽  
pp. 25-30
Author(s):  
Garold Gurevich ◽  
◽  
Sergey Lutmanov ◽  
Oleg Penskiy ◽  
◽  
...  
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Mathematical Models ◽  
Stellar Systems ◽  
Direct And Inverse Problems ◽  
Radiation Sources ◽  
Material Substance

Mathematical models are proposed that allow calculating the coordinates of the centers of equal pressure in stellar systems and solving the inverse problem of determining the radiation sources of a material substance during the formation of macro-bodies. It is shown that the solutions of direct and inverse problems are not unique.

Parametric analysis of static bending of the pipeline

2016 ◽  
Vol 11 (1) ◽  
pp. 24-29 ◽  
Author(s):  
A.A. Yulmukhametov
Keyword(s):  
Inverse Problem ◽  
Pressure Drop ◽  
Inverse Problems ◽  
Internal Pressure ◽  
Parametric Analysis ◽  
Direct And Inverse Problems ◽  
Relative Stiffness

Consideration is given to the direct and inverse problems for pipeline bending both by gravity and transported fluid. The effect of internal pressure drop and the velocity of a fluid are taken into account. The influence of point fixing of “pipeline-capacity” constructions for the deflection is also taken into account. The inverse problem is to determine the relative stiffness of distributed support under the instrument determining pipeline deflection or deformation of its outer fibers. The method of loading pipeline by the concentrated power and determination of appropriate instrument deflection or deformation is applied. In particular, loading and corresponding measurements are carried out at the midpoint of the pipeline span.

PHOTON TRANSPORT PROBLEMS INVOLVING A POINT SOURCE

2007 ◽  
Vol 05 (01) ◽  
pp. 77-93 ◽  
Author(s):  
A. BELLENI-MORANTE ◽  
W. LAMB ◽  
A. C. McBRIDE
Keyword(s):  
Inverse Problem ◽  
Point Source ◽  
Unique Solution ◽  
Cross Section ◽  
Direct Problem ◽  
Interstellar Cloud ◽  
Far Field ◽  
Photon Transport ◽  
Transport Problems ◽  
Photon Source

We consider both a direct and an inverse problem of photon transport in an interstellar cloud with a point photon source. By using a non-rigorous (but physically reasonable) procedure, we prove that the direct problem has a unique solution and that the inverse problem also has a unique solution, under the assumptions that a single value of the photon far-field is known and the scattering cross-section is suitably small. Finally, we show in a rigorous way that the direct problem has a unique distributional solution if the point source is modelled by a Dirac δ functional.

Direct and inverse source problems for a space fractional advection dispersion equation

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Abeer Aldoghaither ◽  
Taous-Meriem Laleg-Kirati ◽  
Da-Yan Liu
Keyword(s):  
Inverse Problem ◽  
Dispersion Equation ◽  
Direct Problem ◽  
Source Term ◽  
Analytic Solution ◽  
Finite Domain ◽  
Inverse Source Problem ◽  
Direct And Inverse Problems ◽  
Advection Dispersion ◽  
Inverse Source Problems

Abstract In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from final observations. We first derive the analytic solution to the direct problem which we use to prove the uniqueness and the unstability of the inverse source problem using final measurements. Finally, we illustrate the results with a numerical example.

An inverse problem for a nonlinear diffusion equation with time-fractional derivative

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Salih Tatar ◽  
Süleyman Ulusoy
Keyword(s):  
Inverse Problem ◽  
Nonlinear Diffusion ◽  
Continuous Dependence ◽  
Direct Problem ◽  
Nonlinear Diffusion Equation ◽  
Unknown Coefficient ◽  
Coefficient Problem ◽  
Inverse Coefficient Problem ◽  
Time Fractional Derivative ◽  
Inverse Coefficient

Abstract A nonlinear time-fractional inverse coefficient problem is considered. The unknown coefficient depends on the solution. It is proved that the direct problem has a unique solution. Afterwards the continuous dependence of the solution of the corresponding direct problem on the coefficient is proved. Then the existence of a quasi-solution of the inverse problem is obtained in the appropriate class of admissible coefficients.

scholarly journals The Regularity of the Solutions of Inverse Problems for the Pseudoparabolic Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 414-424
Author(s):  
Anna Sh. Lyubanova ◽  
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Continuous Dependence ◽  
Input Data ◽  
Order Term ◽  
Unknown Coefficient ◽  
Pseudoparabolic Equation ◽  
Third Order ◽  
Additional Information ◽  
The Third

The paper discusses the regularity of the solutions to the inverse problems on finding unknown coefficients dependent on t in the pseudoparabolic equation of the third order with an additional information on the boundary. By the regularity is meant the continuous dependence of the solution on the input data of the inverse problem. The regularity of the solution is proved for two inverse problems of recovering the unknown coefficient in the second order term and the leader term of the linear pseudoparabolic equation

scholarly journals Problem of Determining a Multidimensional Kernel in One Parabolic Integro–differential Equation

2021 ◽  
pp. 117-127
Author(s):  
Durdimurod K. Durdiev ◽  
Zhavlon Z. Nuriddinov
Keyword(s):  
Differential Equation ◽  
Inverse Problem ◽  
Cauchy Problem ◽  
Direct Problem ◽  
Contractive Mapping ◽  
Equivalent System ◽  
Direct And Inverse Problems ◽  
Integro Differential Equation ◽  
The Cauchy Problem ◽  
The Right

The multidimensional parabolic integro-differential equation with the time-convolution in- tegral on the right side is considered. The direct problem is represented by the Cauchy problem for this equation. In this paper it is studied the inverse problem consisting in finding of a time and spatial dependent kernel of the integrated member on known in a hyperplane xn = 0 for t > 0 to the solution of direct problem. With use of the resolvent of kernel this problem is reduced to the investigation of more convenient inverse problem. The last problem is replaced with the equivalent system of the integral equations with respect to unknown functions and on the bases of contractive mapping principle it is proved the unique solvability to the direct and inverse problems

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