Continuous Dependence on Data for a Solution of Higher Order Quasi-Linear Parabolic Equation Using Fourier Method

Year 2021, Volume: 7 Issue: 2 , 35 - 41 , 09.12.2021

İrem Bağlan , Timur Canel

https://izlik.org/JA49TN88TD

Abstract

In this paper, higher order inverse quasi-linear parabolic problem was investigated. It demonstrated the solution by the Fourier approximation.It proved continuously dependence upon the data of the solution by iteration method.

Keywords

inverse problem , periodic boundary conditions , Fourier method

References

• [1] P.R.Sharma , G. Methi, Solution of two dimensional parabolic equation subject to Non-local conditions using homotopy Perturbation method. Jour. of App.Com. Sci,2012; vol.1:12-16.
• [2] J,R.Cannon , Lin Y., Determination of parameter p(t) in Hölder classes for some semilinear parabolic equations . Inverse Problems.,1989;vol.4:595-606.
• [3] M. Dehghan,Efficient techniques for the second-order parabolic equation subject to nonlocal specifications ,Applied Numerical Mathematics,2005;vol. 52 (1):39-62.
• [4] M. Dehghan,Identifying a control function in two dimensional parabolic inverse problems. Applied Mathematics and Computation,2003; vol .143 (2): 375-391.
• [5] M. Dehghan,Implicit Solution of a Two-Dimensional Parabolic Inverse Problem with Temperature Overspecification,Journal of Computational Analysis and Applications,2001;vol. 3:4.
• [6] N.I. Ionkin , Solution of a boundary-value problem in heat conduction with a nonclassical boundary condition.Differential Equations,1977; vol.13: 204-211.