Geodesic
Regularity and uniqueness in quasilinear parabolic systems
Applications of Mathematics, Tome 56 (2011) no. 4, pp. 341-370.

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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.
DOI : 10.1007/s10492-011-0020-5
Classification : 35A02, 35B65, 35K51, 35K59, 35K60
Keywords: parabolic system; regularity; uniqueness 
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Krejčí, Pavel; Panizzi, Lucia. Regularity and uniqueness in quasilinear parabolic systems. Applications of Mathematics, Tome 56 (2011) no. 4, pp. 341-370. doi : 10.1007/s10492-011-0020-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0020-5/

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