Nonlocal inverse problem for a pseudohyperbolic-pseudoelliptic type differential equation

2021 ◽  
Author(s):  
Tursun K. Yuldashev ◽  
Farhod D. Rakhmonov
Keyword(s):  
Differential Equation ◽  
Inverse Problem ◽  
Type Differential Equation

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

Additional spectral properties of the fourth-order Bessel-type differential equation

2005 ◽  
Vol 278 (12-13) ◽  
pp. 1538-1549 ◽  
Author(s):  
W. N. Everitt ◽  
H. Kalf ◽  
L. L. Littlejohn ◽  
C. Markett
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Spectral Properties ◽  
Type Differential Equation

scholarly journals Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

scholarly journals Illness-Death Model in Chronic Disease Epidemiology: Characteristics of a Related, Differential Equation and an Inverse Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Ralph Brinks
Keyword(s):  
Differential Equation ◽  
Inverse Problem ◽  
Type 1 Diabetes ◽  
Chronic Disease ◽  
Chronic Diseases ◽  
Chronic Disease Epidemiology ◽  
Disease Epidemiology ◽  
Mathematical Relation

Chronic diseases impose a huge burden for mankind. Recently, a mathematical relation between the incidence and prevalence of a chronic disease in terms of a differential equation has been described. In this article, we study the characteristics of this differential equation. Furthermore, we prove the ill-posedness of a related inverse problem arising in chronic disease epidemiology. An example application for the inverse problem about type 1 diabetes in German women aged up to 35 years is given.

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.

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