22 citations · 58 across the 26 of their papers we have counts for
35 papers
An Elementary Perspective on the Dirac Equation and its Closest Relatives
Rainer Picard, Sascha Trostorff, Marcus Waurick
We consider the Dirac equation in a real setting to show its close relationship to Maxwell's equation. In addition to analysing the classical Dirac mass term, we also inspect the a…
Adjoints of sums of m-accretive operators and applications to non-autonomous evolutionary equations
Rainer Picard, Sascha Trostorff, Marcus Waurick
We provide certain compatibility conditions for m-accretive operators such that the adjoint of the sum is given by the closure of the sum of the respective adjoint. We revisit the…
Families of Annihilating Skew-Selfadjoint Operators and their Connection to Hilbert Complexes
Dirk Pauly, Rainer Picard
In this short note we show that Hilbert complexes are strongly related to what we shall call annihilating sets of skew-selfadjoint operators. This provides for a new perspective on…
A Note on Some Non-Local Boundary Conditions and their Use in Connection with Beltrami Fields
Rainer Picard, Sascha Trostorff
We consider two operators between two Hilbert spaces satisfying and and inspect extensions and $B…
M-Accretive Realisations of Skew-Symmetric Operators
Rainer Picard, Sascha Trostorff
We consider skew-symmetric operators on a Hilbert space and characterise all (nonlinear) m-accretive restrictions of in terms of the "deficiency spac…
A Structural Observation on port-Hamiltonian Systems
Rainer Picard, Sascha Trostorff, Bruce Watson +1
We study port-Hamiltonian systems on a familiy of intervals and characterise all boundary conditions leading to -accretive realisations of the port-Hamiltonian operator and thus…
Dynamic First Order Wave Systems with Drift Term on Riemannian Manifolds
Rainer Picard, Sascha Trostorff
An abstract first order differential equation of hyperbolic type with drift term on a Riemannian manifold is considered. For proving its well-posedness, transmutator and commutator…
A Hilbert space approach to fractional differential equations
Kai Diethelm, Konrad Kitzing, Rainer Picard +3
We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on , we defi…
On a Class of Degenerate Abstract Parabolic Problems and Applications to Some Eddy Current Models
Dirk Pauly, Rainer Picard, Sascha Trostorff +1
We present an abstract framework for parabolic type equations which possibly degenerate on certain spatial regions. The degeneracies are such that the equations under investigation…
A Hilbert space approach to difference equations
Konrad Kitzing, Rainer Picard, Stefan Siegmund +2
We consider general difference equations for on exponentially weighted spaces of two-sided Hilbert space valued sequences and dis…
On the Well-posedness of a Class of Non-Autonomous SPDEs: An Operator-Theoretical Perspective
Rainer Picard, Sascha Trostorff, Marcus Waurick
We further elaborate on the solvability of stochastic partial differential equations (SPDEs). We shall discuss non-autonomous partial differential equations with an abstract realiz…
On an Elasto-Acoustic Transmission Problem in Anisotropic, Inhomogeneous Media
Rainer Picard
We consider a coupled system describing the interaction between acoustic and elastic regions, where the coupling occurs not via material properties but through an interaction on an…
On an Electro-Magneto-Elasto-Dynamic Transmission Problem
Rainer Picard
We consider a coupled system describing the interaction between acoustic and elastic regions, where the coupling occurs not via material properties but through an interaction on an…
On Well-Posedness for a Piezo-Electromagnetic Coupling Model with Boundary Dynamics
Rainer Picard
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 enc…
A Note on the Justification of the Eddy Current Model in Electrodynamics
Dirk Pauly, Rainer Picard
The issue of justifying the eddy current approximation of Maxwell's equations is re-considered in the time-dependent setting. Convergence of the solution operators is shown in the…
On Maximal Regularity for a Class of Evolutionary Equations
Rainer Picard, Sascha Trostorff, Marcus Waurick
The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sums of two unbou…
On Boundary Damped Inhomogeneous Timoshenko Beams and Related Problems
Rainer Picard, Bruce A. Watson
We consider the model equations for the Timoshenko beam as a first order system in the framework of evolutionary equations. The focus is on boundary damping, which is implemented a…
On Wellposedness for Some Thermo-Piezo-Electric Coupling Models
Tony Mulholland, Rainer Picard, Sascha Trostorff +1
There is an increasing reliance on mathematical modelling to assist in the design of piezoelectric ultrasonic transducers since this provides a cost-effective and quick way to arri…
A Note on a Two-Temperature Model in Linear Thermoelasticity
Santwana Mukhopadhyay, Rainer Picard, Sascha Trostorff +1
We discuss the so-called two-temperature model in linear thermoelasticity and provide a Hilbert space framework for proving well-posedness of the equations under consideration. Wit…
On Abstract Systems
Rainer Picard, Stefan Seidler, Sascha Trostorff +1
For a large class of dynamical problems from mathematical physics the skew-selfadjointness of a spatial operator of the form $A=\left(\begin{array}{cc} 0 & -C^{*}\\ C & 0 \end{arra…
On Some Models in Linear Thermo-Elasticity with Rational Material Laws
Santwana Mukhopadhyay, Rainer Picard, Sascha Trostorff +1
We shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-pose…
On a Connection between the Maxwell System, the Extended Maxwell System, the Dirac Operator and Gravito-Electromagnetism
Rainer Picard, Sascha Trostorff, Marcus Waurick
Maxwell's equation, Dirac's equation and the equation of gravito-electromagnetism are shown to be particular instances of the extended Maxwell system. The equations are discussed i…
Well-posedness via Monotonicity. An Overview
Rainer Picard, Sascha Trostorff, Marcus Waurick
The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A…
On Some Models for Elastic Solids with Micro-Structure
Rainer Picard, Sascha Trostorff, Marcus Waurick
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. The complexi…