| Abstract: | We study a semilinear parabolic partial differential equation of second order in a bounded domain Ω ? ?N, with nonstandard boundary conditions (BCs) on a part Γnon of the boundary ?Ω. Here, neither the solution nor the flux are prescribed pointwise. Instead, the total flux through Γnon is given, and the solution along Γnon 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 |
