A nonlinear parabolic problem with the Newton boundary conditions and its weak formulation are examined. The problem describes nonstationary heat conduction in inhomogeneous and anisotropic media. We prove a comparison principle which guarantees that for greater data we obtain, in general, greater weak solutions. A new strategy of proving the comparison principle is presented.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-7,
author = {Tomas Vejchodsk\'y},
title = {Comparison principle for a nonlinear parabolic problem of a nonmonotone type},
journal = {Applicationes Mathematicae},
volume = {29},
year = {2002},
pages = {65-73},
zbl = {1014.35044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-7}
}
Tomas Vejchodský. Comparison principle for a nonlinear parabolic problem of a nonmonotone type. Applicationes Mathematicae, Tome 29 (2002) pp. 65-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-7/