Regularity and Uniqueness in quasilinear parabolic systems

0362723 - MÚ 2012 RIV CZ eng J - Journal Article
Krejčí, Pavel - Panizzi, L.
Regularity and Uniqueness in quasilinear parabolic systems.
Applications of Mathematics. Roč. 56, č. 4 (2011), s. 341-370. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA ČR GAP201/10/2315
Institutional research plan: CEZ:AV0Z10190503
Keywords : parabolic system * regularity * uniqueness
Subject RIV: BA - General Mathematics
Impact factor: 0.480, year: 2011
http://www.springerlink.com/content/xkh41744g1975970/

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.
Permanent Link: http://hdl.handle.net/11104/0198966