22 citations · 58 across the 26 of their papers we have counts for
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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…
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…
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…
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 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…
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…
On Evolutionary Equations with Material Laws Containing Fractional Integrals
Rainer Picard, Sascha Trostorff, Marcus Waurick
A well-posedness result for a time-shift invariant class of evolutionary operator equations involving material laws with fractional time-integrals of order is considere…
On Non-Autonomous Evolutionary Problems
Rainer Picard, Sascha Trostorff, Marcus Waurick +1
The paper extends well-posedness results of a previously explored class of time-shift invariant evolutionary problems to the case of non-autonomous media. The Hilbert space setting…
A Note on Fractional Evolutionary Equations
Rainer Picard
A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem cl…
A Class of Evolutionary Problems with an Application to Acoustic Waves with Impedance Type Boundary Conditions
Rainer Picard
A class of evolutionary operator equations is studied. As an application the equations of linear acoustics are considered with complex material laws. A dynamic boundary condition i…
Evolutionary Problems Involving Sturm-Liouville Operators
Rainer Picard, Bruce Watson
The purpose of this paper is to further exemplify an approach to evolutionary problems originally developed in earlier works for a special case and later extended to more general e…
The Elusive Drude-Born-Fedorov Model for Chiral Electromagnetic Media
Henrik Freymond, Rainer Picard
Electro-magnetic wave propagation in more complex linear materials such as bi-anisotropic media have come to a considerable attention within the last fifteen to twenty years. The D…
Mother Operators and their Descendants
Rainer Picard, Sascha Trostorff, Marcus Waurick
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard…