Regularity and uniqueness in quasilinear parabolic systems

Pavel Krejčí; Lucia Panizzi

Applications of Mathematics (2011)

  • Volume: 56, Issue: 4, page 341-370
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Krejčí, Pavel, and Panizzi, Lucia. "Regularity and uniqueness in quasilinear parabolic systems." Applications of Mathematics 56.4 (2011): 341-370. <http://eudml.org/doc/116544>.

@article{Krejčí2011,
abstract = {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.},
author = {Krejčí, Pavel, Panizzi, Lucia},
journal = {Applications of Mathematics},
keywords = {parabolic system; regularity; uniqueness; parabolic system; regularity; uniqueness},
language = {eng},
number = {4},
pages = {341-370},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regularity and uniqueness in quasilinear parabolic systems},
url = {http://eudml.org/doc/116544},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Krejčí, Pavel
AU - Panizzi, Lucia
TI - Regularity and uniqueness in quasilinear parabolic systems
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 4
SP - 341
EP - 370
AB - 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.
LA - eng
KW - parabolic system; regularity; uniqueness; parabolic system; regularity; uniqueness
UR - http://eudml.org/doc/116544
ER -

References

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