On abstract grad–div systems

Abstract

The Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.On Abstract grad-div Systems.Rainer Picard, Stefan Seidler, Sascha Trostorff, Marcus WaurickAbstract. For a large class of dynamical problems from mathematical physics the skew-selfadjointness of a spatial operator of the form A = 0 −C * C 0 , where  is introduced (hence the title). As a particular application we consider a non-standard coupling mechanism and the incorporation of diffusive boundary conditions both modeled by setting associated with a skew-selfadjoint spatial operator A.

On boundary damped inhomogeneous Timoshenko beams and related problems

“…To implement these boundary conditions we consider, in the spirit of abstract grad-div systems as discussed in [6] , the modified system…”

On Boundary Damped Inhomogeneous Timoshenko Beams.

“…To implement these boundary conditions we consider, in the spirit of abstract grad-div systems as discussed in [3] , the associated first order system is…”

On an elasto-acoustic transmission problem in anisotropic‎, ‎inhomogeneous media

“…1 To assume A to be skew-selfadjoint is less restrictive than one might think. For this we note that for example typical dissipative boundary conditions actually give rise to natural skew-selfadjoint spatial operators A, [20]. That skew-selfadjoint A is a quite common assumption but may not be recognized.…”