Comparison principle for a nonlinear parabolic problem of a nonmonotone type
Volume 29 / 2002
Applicationes Mathematicae 29 (2002), 65-73
MSC: Primary 35K55.
DOI: 10.4064/am29-1-7
Abstract
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.
