Related papers: On Well-Posedness for a Piezo-Electromagnetic Coup…
Based on a combination of insights afforded by Rainer Picard and Serge Nicaise, we extend a set of abstract piezo-electromagnetic impedance boundary conditions. We achieve this by accommodating for the influence of heat with the inclusion…
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 interface separating the two regimes. Evolutionary…
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…
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 complexity of physical phenomena appears as encoded in so called…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
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 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 interface separating the two regimes. Evolutionary…
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 consider an initial-boundary value problem for the Maxwell's system in a bounded domain with a linear inhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver-Muller-type boundary feedback mechanism…
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…
This article focuses on the Vlasov-Poisson system with point charges in bounded convex domains, accounting the interactions of point charges with the self-consistent electric field and the boundary, which were not addressed in the previous…
We establish local-in-time and global in time well-posedness for small data, for a coupled system of nonlinear acoustic structure interactions. The model consists of the nonlinear Westervelt equation on a bounded domain with non homogeneous…
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,…
We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the…
We analyze the stability of Maxwell equations in bounded domains taking into account electric and magnetization effects. Well-posedness of the model is obtained by means of semigroup theory. A passitivity assumption guarantees the…
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…
In this paper we consider a nonlinear system of PDEs coupling the viscous Cahn-Hilliard-Oono equation with dynamic boundary conditions enjoying a similar structure on the boundary. After proving well-posedness of the corresponding initial…
We study the well-posedness theory for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors…
We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space…
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…