skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition

Abstract

We consider a quasilinear parabolic system of equations with nondiagonal principal matrix in a model parabolic cylinder with the Neumann condition on the plane part Γ of the lateral surface of the cylinder. We prove the partial regularity (the Hölder continuity) of the weak solution in a neighborhood of Γ by the method of A(t)-caloric approximations adapted to the problem with the Neumann boundary condition.

Authors:
 [1];  [2]
  1. St. Petersburg State University (Russian Federation)
  2. Bauman Moscow State Technical University (Russian Federation)
Publication Date:
OSTI Identifier:
22774003
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 232; Journal Issue: 3; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; BOUNDARY CONDITIONS; CYLINDERS; EQUATIONS; MATHEMATICAL SOLUTIONS; MATRICES; SURFACES

Citation Formats

Arkhipova, A. A., E-mail: arina@AA1101.spb.edu, and Grishina, G. V., E-mail: galinavg@yandex.ru. Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3871-4.
Arkhipova, A. A., E-mail: arina@AA1101.spb.edu, & Grishina, G. V., E-mail: galinavg@yandex.ru. Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition. United States. doi:10.1007/S10958-018-3871-4.
Arkhipova, A. A., E-mail: arina@AA1101.spb.edu, and Grishina, G. V., E-mail: galinavg@yandex.ru. Sun . "Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition". United States. doi:10.1007/S10958-018-3871-4.
@article{osti_22774003,
title = {Regularity of Solutions to Quasilinear Parabolic Systems with Time-Nonsmooth Principal Matrix and the Neumann Boundary Condition},
author = {Arkhipova, A. A., E-mail: arina@AA1101.spb.edu and Grishina, G. V., E-mail: galinavg@yandex.ru},
abstractNote = {We consider a quasilinear parabolic system of equations with nondiagonal principal matrix in a model parabolic cylinder with the Neumann condition on the plane part Γ of the lateral surface of the cylinder. We prove the partial regularity (the Hölder continuity) of the weak solution in a neighborhood of Γ by the method of A(t)-caloric approximations adapted to the problem with the Neumann boundary condition.},
doi = {10.1007/S10958-018-3871-4},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 3,
volume = 232,
place = {United States},
year = {2018},
month = {7}
}