An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition

2021 ◽  
Author(s):  
Mousa J. Huntul ◽  
Mohammad Tamsir ◽  
Neeraj Dhiman
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Fourth Order ◽  
Additional Condition ◽  
Time Dependent ◽  
Dependent Potential

Inverse source problem for parabolic equation with the condition of integral observation in time

2018 ◽  
Vol 26 (4) ◽  
pp. 523-539 ◽  
Author(s):  
Aleksey I. Prilepko ◽  
Vitaly L. Kamynin ◽  
Andrew B. Kostin
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Inverse Problems ◽  
Unique Solvability ◽  
Existence And Uniqueness ◽  
Additional Condition ◽  
Sufficient Conditions ◽  
Inverse Source Problem ◽  
Source Determination ◽  
Integral Observation

Abstract We consider the inverse problem of source determination in nonuniformly parabolic equation under the additional condition of integral observation. We investigate the questions of existence and uniqueness of solution. Two types of sufficient conditions for the unique solvability of the inverse problem are obtained. Examples of inverse problems are given for which the conditions of the proved theorems are fulfilled.

An inverse problem of determining the time-dependent potential in a higher-order Boussinesq-Love equation from boundary data

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mousa Huntul ◽  
Mohammad Tamsir ◽  
Abdullah Ahmadini
Keyword(s):  
Inverse Problem ◽  
Boundary Data ◽  
Numerical Solutions ◽  
Physical Property ◽  
Neumann Boundary ◽  
Higher Order ◽  
Time Dependent ◽  
Potential Coefficient ◽  
Content Type ◽  
Dependent Potential

PurposeThe paper aims to numerically solve the inverse problem of determining the time-dependent potential coefficient along with the temperature in a higher-order Boussinesq-Love equation (BLE) with initial and Neumann boundary conditions supplemented by boundary data, for the first time.Design/methodology/approachFrom the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, the authors apply the generalized finite difference method (GFDM) for solving the BLE along with the Tikhonov regularization to find stable and accurate numerical solutions. The regularized nonlinear minimization is performed using the MATLAB subroutine lsqnonlin. The stability analysis of solution of the BLE is proved using the von Neumann method.FindingsThe present numerical results demonstrate that obtained solutions are stable and accurate.Practical implicationsSince noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.Originality/valueThe knowledge of this physical property coefficient is very important in various areas of human activity such as seismology, mineral exploration, biology, medicine, quality control of industrial products, etc. The originality lies in the insight gained by performing the numerical simulations of inversion to find the potential co-efficient on time in the BLE from noisy measurement.

Direct and inverse problem for the parabolic equation with initial value and time-dependent boundaries

2015 ◽  
Vol 95 (6) ◽  
pp. 1307-1326 ◽  
Author(s):  
Heng Li ◽  
Jianrong Zhou
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Time Dependent ◽  
Initial Value

scholarly journals A Note on the Inverse Problem for a Fractional Parabolic Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Abdullah Said Erdogan ◽  
Hulya Uygun
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Operator Theory ◽  
Source Term ◽  
Approximate Solutions ◽  
Time Dependent ◽  
Stability Estimates ◽  
Theory Approach ◽  
One Dimensional ◽  
Term Stability

For a fractional inverse problem with an unknown time-dependent source term, stability estimates are obtained by using operator theory approach. For the approximate solutions of the problem, the stable difference schemes which have first and second orders of accuracy are presented. The algorithm is tested in a one-dimensional fractional inverse problem.

scholarly journals An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. J. Huntul ◽  
Muhammad Abbas ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Input Data ◽  
Time Dependent ◽  
One Dimensional ◽  
Noisy Input ◽  
Nonlinear Minimization ◽  
Ill Posed ◽  
Dependent Potential ◽  
The Stability ◽  
First Time

AbstractIn this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank–Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.

scholarly journals Determination of a time-dependent coefficient in awave equation with unusual boundary condition

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2653-2665
Author(s):  
Ibrahim Tekin
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Time Dependent ◽  
Conditional Stability ◽  
Small Times ◽  
Dependent Potential ◽  
Initial Boundary Value

In this paper, an initial boundary value problem for a wave equation with unusual boundary condition is considered. Giving an integral over-determination condition, a time-dependent potential is determined and existence and uniqueness theorem for small times is proved. We characterize the estimates of conditional stability of the solution of the inverse problem. Also, the numerical solution of the inverse problem is studied by using finite difference method.

Sign in / Sign up

Export Citation Format

Share Document