Regularity and uniqueness in quasilinear parabolic systems
نویسنده
چکیده
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 di usion coefcient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a re ned variant of the Gronwall lemma.
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