On a comprehensive class of linear control problems

Picard, Rainer; Trostorff, Sascha; Waurick, Marcus

doi:10.1093/imamci/dnu035

Cited by 19 publications

(18 citation statements)

References 30 publications

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“…In Subsect. 3.1 we also prove an energy balance equality by anticipating strategies developed in [32,33]. We recall the results from [27] in Subsect.…”

Section: Introductionmentioning

confidence: 65%

On some models for elastic solids with micro‐structure

2014

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We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory modeling solids with micro-structure. The complexity of physical phenomena appears as encoded in so called material laws. The usefulness of the structural perspective developed is illustrated by showing that many initial boundary value problems in the theory of such elastic solids share the same type of solution theory. Moreover, interconnections of the respective models are discussed via a previously introduced mother/descendant mechanism.

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“…In Subsect. 3.1 we also prove an energy balance equality by anticipating strategies developed in [32,33]. We recall the results from [27] in Subsect.…”

Section: Introductionmentioning

confidence: 65%

On some models for elastic solids with micro‐structure

2014

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“…and of Here L 2 (Ω) 3×3 has a Hilbert space structure unitarily equivalent to L 2 (Ω) 9 . Elements in the domain of the operators marked by a overset circle satisfy an abstract homogeneous boundary condition, which, in case of a sufficiently smooth boundary ∂Ω (e.g.…”

Section: The Basic Systemmentioning

confidence: 99%

On Well-Posedness for a Piezo-Electromagnetic Coupling Model with Boundary Dynamics

Picard

2017

Computational Methods in Applied Mathematics

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We consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces coupled to the partial differential equations. Evolutionary well-posedness, i.e. Hadamard well-posedness and causal dependence on the data, is shown for the resulting model system.

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“…For doing so, we need the following definitions, which are adapted from the abstract boundary data spaces, see e.g. [28,18,19] Definition 2.21. Recall thatc url ⊆ curl, and consequently H(c url, Ω) is a closed subspace of H(curl, Ω).…”

Section: An Abstract Trace Versionmentioning

confidence: 99%

On abstract grad–div systems

Picard¹,

Seidler²,

Trostorff

et al. 2016

Journal of Differential Equations

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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.

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On a comprehensive class of linear control problems

Cited by 19 publications

References 30 publications

On some models for elastic solids with micro‐structure

On some models for elastic solids with micro‐structure

On Well-Posedness for a Piezo-Electromagnetic Coupling Model with Boundary Dynamics

On abstract grad–div systems

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