Abstract: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.
Keywords: parabolic convection-diffusion equation, nonlinear Newton boundary condition, Galerkin method, compactness method, finite element approximation, error estimates
AMS Subject Classification: 35K60, 65N30, 65N15