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A nonlinear parabolic equation with a nonlocal boundary term

✍ Scribed by Marián Slodička; Sofiane Dehilis

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 491 KB
Volume: 233
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.07.059

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✦ Synopsis

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.

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