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

Year 2020, Volume: 5 Issue: 3, 214 - 219, 30.12.2020

İrem Bağlan , Timur Canel

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] 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] 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] 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] M. Dehghan,Identifying a control function in two dimensional parabolic inverse problems. Applied Mathematics and Computation,2003; vol .143 (2): 375-391.
• [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] 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] 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] 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] 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] F.Kanca ,I. Baglan ,An inverse coefficient problem for a quasilinear parabolic equation with nonlocal boundary conditions, Boundary Value Problems , 2013, V.213.
• [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.