Continuous Dependence on Data for a Solution of determination of an unknown source of Heat Conduction of Poly(methyl methacrylate) (PMMA)

Abstract

In this paper,we consider a coefficient problem of an inverse problem of a quasilinear parabolic equation with periodic boundary and integral over determination conditions.It showed the stability of the solution by iteration method and examined numerical solution.

Keywords

• Quasilinear Parabolic Equation
• Inverse Problem
• Periodic Boundary Condition

References

1. 1] J,R.Cannon , Y.Lin , Determination of parameter p(t) in Hölder classes for some semilinear parabolic equations. Inverse Problems, 1988, 4:595-606.
2. [2] R.Pourgholia , M.Rostamiana and M.Emamjome, A numerical method for solving a nonlinear inverse parabolic problem. Inverse Problems in Science and Engineering, 2010, 18(8):1151-1164.
3. [3] P.R.Sharma , G. Methi, Solution of two dimensional parabolic equation subject to Non-local conditionsusing homotopy Perturbation method. Jour. of App.Com. Sci,2012; vol.1:12-16.
4. [4] M. Dehghan,Identifying a control function in two dimensional parabolic inverse problems. Applied Mathematics and Computation,2003; vol .143 (2): 375-391.
5. [5] E. Set, A.O. Akdemir, B. Çelik, On Generalization of Fejér Type Inequalities via fractional integral opera-tor,2018, Filomat, Vol 32: Issue 16.
6. [6] A.O. Akdemir, E. Set and A. Ekinci, On new conformable fractional integral inequalities for product ofdi¤erent kinds of convexity, TWMS Journal of Applied and Engineering Mathematics,2019, Vol 9, Issue 1,142-150.
7. [7] A. ERGÜN, "TheMultiplicity of Eigenvalues of a Vectorial Diffusion Equations with Discontinuous Function Inside A Finite Interval", Turkish Journal of Science, Volume 5, Issue 2, 73-84, 2020.
8. [8] A. Ergün and R. Amirov, “Direct and Inverse problems for diffusion operator with discontinuıty points,” Journal of Applied and Engineering Mathematics, vol. 9, no. 1, pp. 9–21, Jan. 2019.

9. [9] A. Ergün, “Integral Representation for Solution of Discontinuous Diffusion Operator with Jump Conditions,” Cumhuriyet Science Journal, vol. 39, no. 4, pp. 842–863, Jul. 2018.
10. [10] F.Kanca ,I. Baglan ,An inverse coefficient problem for a quasilinear parabolic equation with nonlocal boundary conditions, Boundary Value Problems , 2013, V.213.
11. [11] F.Kanca ,I.Baglan ,An inverse problem for a quasilinear parabolic equation with nonlocal boundary and overdetermination conditions, Journal of inequalities and applications, 2014, V.76.