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This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a bounded domain in $\mathbb R^d$ ($d\ge3$) with a smooth…
We demonstrate and explain that conventional finite difference schemes for direct numerical integration do not approximate the continuum Kardar-Parisi-Zhang (KPZ) equation due to microscopic roughness. The effective diffusion coefficient is…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate…
We give an approach to exponential stability within the framework of evolutionary equations due to [R. Picard. A structural observation for linear material laws in classical mathematical physics. Math. Methods Appl. Sci.,…
The main purpose of this paper is to formulate new conditions for smooth linearization of nonautonomous systems with discrete and continuous time. Our results assume that the linear part admits a very general form of dichotomy known as…
Let $\Lambda^{\mathbb{R}}$ denote the linear space over $\mathbb{R}$ spanned by $z^{k}$, $k \! \in \! \mathbb{Z}$. Define the real inner product (with varying exponential weights) $\langle \boldsymbol{\cdot},\boldsymbol{\cdot}…
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…
Stochastic partial differential equations (SPDEs) have become a crucial ingredient in a number of models from economics and the natural sciences. Many SPDEs that appear in such applications include non-globally monotone nonlinearities.…
The Kochen-Specker theorem states that a 3-dimensional complex Euclidean space admits a finite configuration of projective lines such that the corresponding quantum observables (the orthogonal projectors) cannot be assigned with 0 and 1…
In this article we investigate the solvability of infinite-dimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the state-space that leads to an…
This paper provides a finite sample bound for the error term in the Edgeworth expansion for a sum of independent, potentially discrete, nonlattice random vectors, using a uniform-in-$P$ version of the weaker Cram\'{e}r condition in Angst…
We study skew-orthogonal polynomials with respect to the weight function $\exp[-2V(x)]$, with $V(x)=\sum_{K=1}^{2d}(u_{K}/{K})x^{K}$, $u_{2d} > 0$, $d > 0$. A finite subsequence of such skew-orthogonal polynomials arising in the study of…
We consider the numerical approximation of a general second order semi--linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media which is fundamental in many…
We extend projection theorems concerning Hellinger and Jones et al. divergences to the continuous case. These projection theorems reduce certain estimation problems on generalized exponential models to linear problems. We introduce the…
In this paper, we investigate a class of doubly nonlinear evolutions PDEs. We establish sharp regularity for the solutions in H\"older spaces. The proof is based on the geometric tangential method and intrinsic scaling technique. Our…
In this article we characterize the extreme points of the unit ball of a non-commutative (quantum) Lorentz space associated with a semi-finite von Neumann algebra. This enables us to show that surjective isometries between non-commutative…
A major result concerning perturbations of integrable Hamiltonian systems is given by Nekhoroshev estimates, which ensures exponential stability of all solutions provided the system is analytic and the integrable Hamiltonian not too…
The main goal of this article is to study a Calder\'on type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the…
We give a complete analysis of the projective unitary irreducible representations of the Poincar\'e group in 1+2 dimensions applying Mackey theorem and using an explicit formula for the universal covering group of the Lorentz group in 1+2…