Regularity and Uniqueness in quasilinear parabolic systems

0362723 - MÚ 2012 RIV CZ eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GAP201/10/2315
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: parabolic system * regularity * uniqueness
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.480, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0198966