Browsing by Author "935aa2d31aa740a4a22250aab6c8976b"
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An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition
In this paper the inverse problem of finding the timedependent coefficient of heat capacity together with the solution periodic boundary and integral overdetermination conditions is considered. Under some natural regularity and consistency conditions on the input data the existence uniqueness and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example. Copyright (c) 2014 John Wiley & Sons Ltd.

An inverse problem for a quasilinear parabolic equation with nonlocal boundary and overdetermination conditions
Authors:Kanca, Fatma; Bağlan, İrem Sakınç
Publisher and Date:(Springer International Publishing Ag, 2014)In this paper the inverse problem of finding the timedependent coefficient of heat capacity together with the solution of heat equation with nonlocal boundary conditions is considered. Under some natural regularity and consistency conditions on the input data the existence uniqueness and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example.

Determination of an Unknown Heat Source from Integral Overdetermination Condition
Authors:Baglan, İrem Sakınç; Kanca, Fatma; Mishra, Vishnu Narayan
Publisher and Date:(Springer International Publishing, 2018)In this research we consider a coefficient problem of an inverse problem of a quasilinear parabolic equation with periodic boundary and integral over determination conditions. We prove the existence uniqueness and continuously dependence upon the data of the solution by iteration method. Also we consider numerical solution for this inverse problem using linearization and finite difference method is proved.

Generalized and numerical solution for a quasilinear parabolic equation with nonlocal conditions
In this paper we study the one dimensional mixed problem with nonlocal boundary conditions for the quasilinear parabolic equation. We prove an existence uniqueness of the weak generalized solution and also continuous dependence upon the data of the solution are shown by using the generalized Fourier method. We construct an iteration algorithm for the numerical solution of this problem. We analyze computationally convergence of the iteration algorithm as well as on test example.

Twodimensional inverse quasilinear parabolic problem with periodic boundary condition
In this study we consider a coefficient problem of a quasilinear twodimensional parabolic inverse problem with periodic boundary and integral over determination conditions. We prove the existence uniqueness and continuously dependence upon the data of the solution by iteration method. Also we consider numerical solution for this inverse problem by using linearization and the implicit finitedifference scheme.

Weak generalized and numerical solution for a quasilinear pseudoparabolic equation with nonlocal boundary condition
Authors:Bağlan, İrem Sakınç; Kanca, Fatma
Publisher and Date:(Springer International Publishing, 2014)This paper investigates the one dimensional mixed problem with nonlocal boundary conditions for the quasilinear parabolic equation. Under some natural regularity and consistency conditions on the input data the existence uniqueness convergence of the weak generalized solution and also continuous dependence upon the data of the solution are shown by using the generalized Fourier method. We construct an iteration algorithm for the numerical solution of this problem.