On Solvability of Dissipative Partial Differential-Algebraic Equations
Birgit Jacob, Kirsten Morris
Abstract
We investigate the solvability of infinitedimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the state-space that leads to an extension of the Hille-Yosida Theorem on reflexive Banach spaces is described. For dissipative partial differential equations the Lumer-Phillips generation theorem characterizes solvability and also boundedness of the associated semigroup. An extension of the Lumer-Phillips generation theorem to dissipative differential-algebraic equations is given. The results are illustrated by coupled systems and the Dzektser equation.
Topics & Concepts
MathematicsDissipative systemC0-semigroupDifferential algebraic geometryDifferential algebraic equationBanach spaceDissipative operatorPartial differential equationDifferential equationStochastic partial differential equationSemigroupAlgebraic differential equationAlgebraic numberMathematical analysisPure mathematicsOrdinary differential equationPhysicsQuantum mechanicsNumerical methods for differential equationsStability and Controllability of Differential EquationsQuantum chaos and dynamical systems