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Semilinear parabolic problem with nonstandard boundary conditions: Error estimates
Author(s) -
Slodička Marián
Publication year - 2003
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10035
Subject(s) - mathematics , pointwise , bounded function , boundary (topology) , mathematical analysis , parabolic partial differential equation , partial differential equation , domain (mathematical analysis) , boundary value problem , constant (computer programming) , space (punctuation) , function (biology) , partial derivative , order (exchange) , linguistics , philosophy , finance , evolutionary biology , computer science , economics , biology , programming language
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