On a Nonlinear Initial—Boundary Value Problem with Venttsel Type Boundary Conditions Arizing in Homogenization of Complex Heat Transfer Problems

We consider a non-standard nonlinear singularly perturbed 2D initial-boundary value problem with Venttsel type boundary conditions, arising in homogenization of radiative-conductive heat transfer problems. establish existence, uniqueness and regularity weak solution v. obtained estimates for the derivatives Dtv, D12v, D22v, D1D2v qualified order small parameter ε.