Regularity and uniqueness in quasilinear parabolic systems
- Krejčí, Pavel
- Panizzi, Lucia
2010 Mathematics Subject Classification
- 35K50 35K60
- Parabolic system, regularity, uniqueness
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.