Geodesic
Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates
Applications of Mathematics, Tome 48 (2003) no. 1, pp. 49-66.

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In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain $\Omega \subset \mathbb{R}^N$, with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant $\alpha (t)$, accompanied with a nonlocal (integral) Dirichlet side condition. We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution $u$ and also of the unknown function $\alpha $.
DOI : 10.1023/A:1022954920827
Classification : 35B30, 35K20, 35K55, 65M15, 65M32
Keywords: nonlocal boundary condition; parameter identification; parabolic IBVP 
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     title = {Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: {Error} estimates},
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Slodička, Marián. Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates. Applications of Mathematics, Tome 48 (2003) no. 1, pp. 49-66. doi : 10.1023/A:1022954920827. http://geodesic.mathdoc.fr/articles/10.1023/A:1022954920827/

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