Existence and uniqueness of an inverse problem for a hyperbolic system of lidar probing (cloud properties)

1992 ◽  
Vol 8 (6) ◽  
pp. 821-829 ◽  
Author(s):  
Dat Duc Bui ◽  
P Nelson
Keyword(s):  
Inverse Problem ◽  
Hyperbolic System ◽  
Existence And Uniqueness ◽  
Cloud Properties

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.

scholarly journals An inverse problem for a hyperbolic system on a vector bundle and energy measurements

2011 ◽  
Vol 354 (4) ◽  
pp. 1431-1464
Author(s):  
Katsiaryna Krupchyk ◽  
Matti Lassas
Keyword(s):  
Inverse Problem ◽  
Vector Bundle ◽  
Hyperbolic System

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 Determination of a control parameter in a parabolic partial differential equation

1991 ◽  
Vol 33 (2) ◽  
pp. 149-163 ◽  
Author(s):  
J. R. Cannon ◽  
Yanping Lin ◽  
Shingmin Wang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Global Solution ◽  
Existence And Uniqueness ◽  
Control Parameter ◽  
Parabolic Partial Differential Equation ◽  
Solution Pair ◽  
Image Position

AbstractThe authors consider in this paper the inverse problem of finding a pair of functions (u, p) such thatwhere F, f, E, s, αi, βi, γi, gi, i = 1, 2, are given functions.The existence and uniqueness of a smooth global solution pair (u, p) which depends continuously upon the data are demonstrated under certain assumptions on the data.

Existence and uniqueness of an inverse problem for nonlinear Klein‐Gordon equation

2019 ◽  
Vol 42 (10) ◽  
pp. 3739-3753
Author(s):  
Ibrahim Tekin ◽  
Yashar T. Mehraliyev ◽  
Mansur I. Ismailov
Keyword(s):  
Inverse Problem ◽  
Existence And Uniqueness ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

Inverse problems of mixed type in linear plate theory

2004 ◽  
Vol 15 (2) ◽  
pp. 129-146 ◽  
Author(s):  
DOMINGO SALAZAR ◽  
REX WESTBROOK
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Plate Theory ◽  
Order Partial Differential Equation ◽  
General Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Sag Bending

The characterisation of those shapes that can be made by the gravity sag-bending manufacturing process used to produce car windscreens and lenses is modelled as an inverse problem in linear plate theory. The corresponding second-order partial differential equation for the Young's modulus is shown to change type (possibly several times) for certain target shapes. We consider the implications of this behaviour for the existence and uniqueness of solutions of the inverse problem for some frame geometries. In particular, we show that no general boundary conditions for the inverse problem can be prescribed if it is desired to achieve certain kinds of target shapes.

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