(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Krejčí, Pavel; Panizzi, Lucia
Inspired by a problem in steel metallurgy, we prove the existence,
regularity, uniqueness, and continuous data dependence of solutions to a
coupled parabolic system in a smooth bounded 3D domain, with nonlinear and
nonhomogeneous boundary conditions. The nonlinear coupling takes place in the
diffusion coefficient. The proofs are based on anisotropic estimates in
tangential and normal directions, and on a refined variant of the Gronwall
lemma.
