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Semilinear parabolic problem with nonstandard boundary conditions: Error estimates

✍ Scribed by Marián Slodička

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
195 KB
Volume
19
Category
Article
ISSN
0749-159X

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✦ Synopsis

Abstract

We study a semilinear parabolic partial differential equation of second order in a bounded domain Ω ⊂ ℝ^N^, with nonstandard boundary conditions (BCs) on a part Γ~non~ of the boundary ∂Ω. Here, neither the solution nor the flux are prescribed pointwise. Instead, the total flux through Γ~non~ is given, and the solution along Γ~non~ has to follow a prescribed shape function, apart from an additive (unknown) space‐constant α(t). We prove the well‐posedness of the problem, provide a numerical method for the recovery of the unknown boundary data, and establish the error estimates. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 167–191, 2003

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