Natural and Applied Sciences Journal2645-9000İzmir Demokrasi ÜniversitesiStability of Solution of Quasilinear Parabolic Two-Dimensional with Inverse Coefficient by Fourier MethodBağlanİremkocaeli üniversitesihttps://orcid.org/0000-0002-1877-979110.38061/idunas.1296023Mathematical SciencesMatematik07042023619200511202306192023In this article, the heat inverse two-dimensional quasilinear parabolic problem is examined. The stability and numerical solution for the problem are discussed.Since the problem is not linear, Picard's successive approximations theorem is used. In the numerical part, the solution is made with the finite difference and linearization method.Inverse problem Fourier method Periodic boundary conditions Picard Method Two dimension parabolic problem Fourier coefficient.1. Sharma, P.R., Methi, G. (2012). Solution of two-dimensional parabolic equation subject to non-local conditions using homotopy Perturbation method, Jour. of App.Com., 1, 12-16.2. Cannon, J. Lin, Y. (1899). Determination of parameter p(t) in Hölder classes for some semi linear parabolic equations, Inverse Problems, 4, 595-606.3. Dehghan, M. (2005). Efficient techniques for the parabolic equation subject to nonlocal specifications, Applied Numerical Mathematics, 52(1), 39-62,2005.4. Dehghan, M. (2001). Implicit Solution of a Two-Dimensional Parabolic Inverse Problem with Temperature Overspecification, Journal of Computational Analysis and Applications, 3(4).5. Bağlan, I., Kanca, F. (2020). Solution of the boundary-value problem of heat conduction wıth periodic boundary conditions, Ukrainian Mathematical Journal, 72(2), 232-245.6. Bağlan, I., Kanca, F. (2020). Two-dimensional inverse quasilinear parabolic problems with periodic boundary conditions of the boundary-value problem of heat conduction with periodic boundary conditions, Applicable Analysis, 98(8), 1549-1565.7. Ionkin, N.I. (1977). Solution of a boundary value problem in heat conduction with a nonclassical boundary condition, Differential Equations, 13, 204-211.8. Hill G.W. (1886), On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon, Acta Mathematica, 8,1-36.