Geodesic
On a parabolic problem with nonlinear Newton boundary conditions
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 429-455 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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 
@article{CMUC_2002_43_3_a3,
     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},
     year = {2002},
     volume = {43},
     number = {3},
     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/