Regularity and uniqueness in quasilinear parabolic systems. (Q642212)

Inspired by a problem in steel metallurgy, the authors 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. According to my opinion this is a very nice paper which addresses real world applications and uses modern mathematical methods at the same time.