Comparison principle for a nonlinear parabolic problem of a nonmonotone type

Volume 29 / 2002

Tomas Vejchodský Applicationes Mathematicae 29 (2002), 65-73 MSC: Primary 35K55. DOI: 10.4064/am29-1-7


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.


  • Tomas VejchodskýMathematical Institute
    Academy of Sciences
    Žitná 25
    CZ-11567, Praha 1, Czech Republic

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