Uniqueness of a solution of the inverse problem for the evolution equation and application to the transport equation

1992 ◽  
Vol 51 (2) ◽  
pp. 158-165 ◽  
Author(s):  
A. I. Prilepko ◽  
I. V. Tikhonov
Keyword(s):  
Inverse Problem ◽  
Evolution Equation ◽  
Transport Equation ◽  
Uniqueness Of A Solution

Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Zakaria Faiz ◽  
Driss El Moutawakil
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Frictional Contact ◽  
Hemivariational Inequalities ◽  
Frictional Contact Problem ◽  
Uniqueness Of A Solution

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

An inversion formula for the transport equation in ℝ3 using complex analysis in several variables

2019 ◽  
Vol 27 (3) ◽  
pp. 341-352
Author(s):  
Seyed Majid Saberi Fathi
Keyword(s):  
Inverse Problem ◽  
Transport Equation ◽  
Inversion Formula ◽  
Complex Analysis ◽  
Three Dimensional ◽  
Analytical Continuation ◽  
Radon Transforms ◽  
Photon Transport ◽  
X Ray ◽  
Several Variables

Abstract In this paper, the stationary photon transport equation has been extended by analytical continuation from {\mathbb{R}^{3}} to {\mathbb{C}^{3}} . A solution to the inverse problem posed by this equation is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transforms, respectively. We show that these results can be transformed into each other, and they agree with known results. Numerical reconstructions of a three-dimensional Shepp–Logan head phantom using the obtained inverse formula illustrate the analytical results obtained in this manuscript.

An inverse problem for an evolution equation

1991 ◽  
Vol 49 (5) ◽  
pp. 535-540 ◽  
Author(s):  
Yu. S. �idel'man
Keyword(s):  
Inverse Problem ◽  
Evolution Equation

scholarly journals An Inverse Problem for a Class of Linear Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Yuhuan Zhao
Keyword(s):  
Inverse Problem ◽  
Evolution Equation ◽  
Evolution Equations ◽  
Optimal Parameter ◽  
Optimization Method ◽  
Necessary Condition ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Fréchet Differentiable

An inverse problem for a linear stochastic evolution equation is researched. The stochastic evolution equation contains a parameter with values in a Hilbert space. The solution of the evolution equation depends continuously on the parameter and is Fréchet differentiable with respect to the parameter. An optimization method is provided to estimate the parameter. A sufficient condition to ensure the existence of an optimal parameter is presented, and a necessary condition that the optimal parameter, if it exists, should satisfy is also presented. Finally, two examples are given to show the applications of the above results.

scholarly journals On an inverse problem for fractional evolution equation

2017 ◽  
Vol 6 (1) ◽  
pp. 111-134
Author(s):  
Nguyen Huy Tuan ◽  
◽  
Mokhtar Kirane ◽  
Long Dinh Le ◽  
Van Thinh Nguyen ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Evolution Equation ◽  
Fractional Evolution Equation

scholarly journals Inverse problem for transport equation of ultra-high energy cosmic rays

2013 ◽  
Vol 409 ◽  
pp. 012065
Author(s):  
V S Ptuskin ◽  
S I Rogovaya ◽  
V N Zirakashvili ◽  
E G Klepach
Keyword(s):  
Inverse Problem ◽  
Cosmic Rays ◽  
Transport Equation ◽  
High Energy ◽  
Ultra High Energy ◽  
High Energy Cosmic Rays
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