Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2004 · 31 citations · 0 references
Natural SciencesMathematicsDifferential EquationsBoundary ConditionsBoundary-value ProblemsInitial ConditionsInitial Value ProblemsPartial Differential EquationsVariational InequalitiesEnergyEnergy EstimatesInitial Boundary ConditionsInitial-boundary Value ProblemsNonlinear Initial Value ProblemsOperator InequalitiesParabolic Boundary-value ProblemsParabolic Partial Differential Equations
We study a class of initial-boundary-value problems for which an auxiliary condition of the form is prescribed. We determine bounds on an energy expression by means of differential inequalities and derive pointwise bounds for the solution and its gradient by use of a parabolic maximum principle.