Geodesic
On a parabolic problem with nonlinear Newton boundary conditions
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 429-455

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The paper is concerned with the study of a parabolic initial-boundary value problem with nonlinear Newton boundary condition considered in a two-dimensional domain. The goal is to prove the existence and uniqueness of a weak solution to the problem in the case when the nonlinearity in the Newton boundary condition does not satisfy any monotonicity condition and to analyze the finite element approximation.
Classification : 35A35, 35D05, 35K57, 35K60, 65M60, 65N15, 65N30
Keywords: parabolic convection-diffusion equation; nonlinear Newton boundary condition; Galerkin method; compactness method; finite element approximation; error estimates 
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     author = {Feistauer, Miloslav and Najzar, Karel and \v{S}vadlenka, Karel},
     title = {On a parabolic problem with nonlinear {Newton} boundary conditions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {429--455},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2002},
     mrnumber = {1920519},
     zbl = {1090.35102},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002__43_3_a3/}
}
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Feistauer, Miloslav; Najzar, Karel; Švadlenka, Karel. On a parabolic problem with nonlinear Newton boundary conditions. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 429-455. http://geodesic.mathdoc.fr/item/CMUC_2002__43_3_a3/