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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…
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 arrive at a first prototype. Given a desired operating envelope…
This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
In this contribution, a stochastic nonlinear evolution system under Neumann boundary conditions is investigated. Precisely, we are interested in finding an existence and uniqueness result for a random heat equation coupled with a…
Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
We derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity,…
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…
We study the well-posedness and stability of an impedance passive infinite-dimensional linear system under nonlinear feedback of the form $u(t)=\phi(v(t)-y(t))$, where $\phi$ is a monotone function. Our first main result introduces…
In this paper, we consider a free boundary problem of the incompressible elatodynamics, a coupling system of the Euler equations for the fluid motion with a transport equation for the deformation tensor. Under a natural force balance law on…
We study the well-posedness and asymptotic behaviour of selected PDE-PDE and PDE-ODE systems on one-dimensional spatial domains, namely a boundary coupled wave-heat system and a wave equation with a dynamic boundary condition. We prove…
We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…
These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of…
We study linear integro-differential equations in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations are covered by the class of…
We analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular…
In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…
The purpose of this paper is to demonstrate how different types of boundary conditions do not impact the asymptotic behaviour of the solutions of thermoelastic wave model. For an initial-boundary value problem associated with this system,…
In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a natural stability condition, which ensures that the evolution equation describing the free boundary is strictly…
We extend to incremental thermoelectroelasticity with biasing fields certain classical theorems, that have been stated and proved in linear thermopiezoelectricity referred to a natural configuration. A uniqueness theorem for the solutions…