Browsing by Subject "Nonlocal boundary condition"
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Determination of a diffusion coefficient in a quasilinear parabolic equation
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Publisher and Date:(De Gruyter Open Ltd, 2017)This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence uniqueness and continuously dependence upon the data of the solution are shown. Finally some numerical experiments are presented.
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Generalized and numerical solution for a quasilinear parabolic equation with nonlocal conditions
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Publisher and Date:(Univ Babes-Bolyai, 2015)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.
