Related papers: On General Balance Laws with Boundary
This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear…
In gauge/gravity duality, points which are not causally related on the boundary cannot be causally related through the bulk; this is the statement of boundary causality. By the Gao-Wald theorem, the averaged null energy condition in the…
In this paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy…
The recently established generalized Gell-Mann--Low theorem is applied in lowest perturbative order to bound-state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann--Low Theorem…
In previous work, we derived new energy and entropy stable open boundary conditions and implementation procedures for linear and nonlinear initial boundary value problems. These boundary procedures results in estimates bounded by external…
We prove well posedness and stability in $\mathbf{L}^1$ for a class of mixed hyperbolic-parabolic non linear and non local equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the…
We study quadrangular properties of binary relations on a set $X$~--i.e., properties defined on configurations of four elements--~within an agonistic interpretation, where $xRy$ is interpreted as $x$ ``attacks''~$y$. Such relations induce a…
This paper is concerned with the initial-boundary value problem for an evolutionary variational inequality complying with three intrinsic properties: complete irreversibility, unilateral equilibrium of an energy and an energy conservation…
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
The goal of this article is to discuss a recent conjecture of the two authors, which aims to describe the long time behavior of solutions to one-dimensional dispersive equations with cubic and higher nonlinearities. These problems arguably…
We investigate in the paper general (not necessarily definite) canonical systems of differential equation in the framework of extension theory of symmetric linear relations. For this aim we first introduce the new notion of a boundary…
We prove the local boundedness for solutions to a class of obstacle problems with non-standard growth conditions. The novelty here is that we are able to establish the local boundedness under a sharp bound on the gap between the growth…
The main aim of the note is to provide an upper-bound for the characteristic number of conic-line arrangements with ordinary singularities in the complex projective plane.
I have applied multiple-scale perturbation theory to a generalized complex $PT$-symmetric Mathieu equation in order to find the stability boundaries between bounded and unbounded solutions. The analysis suggests that the non-Hermitian…
We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…
A persistent challenge in numerical relativity is the correct specification of boundary conditions. In this work we consider a many parameter family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein…
The main goal of this paper is to show that the blow up phenomenon (the explosion of the $ \rL^{\infty }$-norm) of the solutions of several classes of evolution problems can be controlled by means of suitable global controls $\alpha (t)$…
The study of blow-up solution of time-fractional heat equations is of significant and wide-ranging interest for its multitude of applications. These types of equations are used to model several real problems in science and engineering. This…
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such…