Related papers: Transparent numerical boundary conditions for evol…
In this paper, we consider a fully-discrete approximation of an abstract evolution equation deploying a non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of the…
These Notes are intended for graduate or undergraduate students who have familiarity with Lebesgue measure theory, partial differential equations, and functional analysis. The main topics covered in this work are the study of the Cauchy…
The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over R^d and in L^p-spaces with respect to tight evolution systems of measures. Here, the linear part…
Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…
A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary…
Numerical solution of equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes for the time evolution. A predefined grid in the problem domain and a…
In this paper we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of…
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…
The question of whether features and behaviors that are characteristic to completely integrable systems persist in the transition to non-integrable settings is a central one in the field of nonlinear dispersive equations. In this work, we…
We investigate the evolution of localized initial value profiles when propagated in integrable versions of higher time-derivative theories. In contrast to the standard cases in nonlinear integrable systems, where these profiles evolve into…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
Domain decomposition methods are essential in solving applied problems on parallel computer systems. For boundary value problems for evolutionary equations the implicit schemes are in common use to solve problems at a new time level…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
We consider the problem of absence of backscattering in the transport of Manakov solitons on a line. The concept of transparent boundary conditions is used for modeling the reflectionless propagation of Manakov vector solitons in a…
In the context of integrable partial difference equations on quad-graphs, we introduce the notion of open boundary reductions as a new means to construct discrete integrable mappings and their invariants. This represents an alternative to…
We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the…
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…