Generalized and numerical solution for a quasilinear parabolic equation with nonlocal conditions

Abstract

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.