REGULARITY AND UNIQUENESS IN QUASILINEAR PARABOLIC SYSTEMS

被引：9

作者：

Krejci, Pavel ^{[1
]}

Panizzi, Lucia ^{[2
]}

机构：

[1] Acad Sci Czech Republic, Inst Math, CR-11567 Prague 1, Czech Republic

[2] Tech Univ Darmstadt, Fachbereich Math, D-64289 Darmstadt, Germany

来源：

APPLICATIONS OF MATHEMATICS | 2011年 / 56卷 / 04期

关键词：

parabolic system; regularity; uniqueness;

D O I：

10.1007/s10492-011-0020-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：341 / 370

页数：30

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