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parabolic convection-diffusion equation; nonlinear Newton boundary condition; Galerkin method; compactness method; finite element approximation; error estimates
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.
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