6 research outputs found
How to get a conservative well-posed linear system out of thin air. Part II. Controllability and stability
Published versio
Grushin problems and control theory: Formulation and examples
In this paper we give a new formulation of an abstract control problem in
terms of a Grushin problem, so that we will reformulate all notions of
controllability, observability and stability in a new form that gives readers
an easy interpretation of these notions
Feedback theory extended for proving generation of contraction semigroups
Recently, the following novel method for proving the existence of solutions
for certain linear time-invariant PDEs was introduced: The operator associated
to a given PDE is represented by a (larger) operator with an internal loop. If
the larger operator (without the internal loop) generates a contraction
semigroup, the internal loop is accretive, and some non-restrictive technical
assumptions are fulfilled, then the original operator generates a contraction
semigroup as well. Beginning with the undamped wave equation, this general idea
can be applied to show that the heat equation and wave equations with damping
are well-posed. In the present paper we show how this approach can benefit from
feedback techniques and recent developments in well-posed systems theory, at
the same time generalising the previously known results. Among others, we show
how well-posedness of degenerate parabolic equations can be proved.Comment: 33 page