A nonlinear parabolic equation with a nonlocal boundary term

Authors:
Marián Slodička;Sofiane Dehilis
Affiliations:
Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Gent, Belgium;Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Gent, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

A nonlinear parabolic problem with a nonlocal boundary condition is studied. We prove the existence of a solution for a monotonically increasing and Lipschitz continuous nonlinearity. The approximation method is based on Rothe's method. The solution on each time step is obtained by iterations, convergence of which is shown using a fixed-point argument. The space discretization relies on FEM. Theoretical results are supported by numerical experiments.