Related papers: Delay Equations of the Wheeler-Feynman Type
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
In this paper we study a class of semilinear wave type equations with viscoelastic damping and delay feedback with time variable coefficient. By combining semigroup arguments, careful energy estimates and an iterative approach we are able…
The Fornberg-Whitham (FW) equation was introduced by Fornberg and Whitham [Fornberg and Whitham, Phil. Trans. R. Soc. Lond. A (1978)] as a nonlocal model for unidirectional shallow water waves capable of capturing wave steepening and…
In the context of the Feynman's derivation of electrodynamics, we show that noncommutativity allows other particle dynamics than the standard formalism of electrodynamics.
We consider several models of State Dependent Delay Differential Equations (SDDEs), in which the delay is affected by a small parameter. This is a very singular perturbation since the nature of the equation changes. Under some conditions,…
Wheeler's delayed-choice experiment was conceived to illustrate the paradoxical nature of wave-particle duality in quantum mechanics. In the experiment, quantum light can exhibit either wave-like interference patterns or particle-like…
Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.
In our adjacent work, we developed a spectral comparison principle for compound cocycles generated by delay equations. It allows to derive frequency inequalities for the uniform exponential stability of such cocycles by means of their…
We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a Yang-Mills field, with or without mass term, if the spatial geometry of the underlying spacetime is homothetic to $\R[3]$.…
Original Whitham's method of derivation of modulation equations is applied to systems whose dynamics is described by a perturbed Korteweg-de Vries equation. Two situations are distinguished: (i) the perturbation leads to appearance of…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
We study wormhole as the solution of the Wheeler-deWitt (WdW ) equation satisfying Hawking-Page wormhole boundary conditions in Friedmann-Robertson-Walker (FRW) cosmology. The quantum wormholes are formulated with arbitrary factor ordering…
This note states and proves an integral representation formula of the ``variation-of-constant'' type for continuous solutions of linear non-autonomous difference delay systems, in terms of a Lebesgue-Stieltjes integral involving a…
The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole…
This paper first propose a concept of Weyl double-measure pseudo-almost automorphic functions and examines their fundamental characteristics. Subsequently, employing fixed point theorems, we systematically investigate the existence and…
We consider the spectral decomposition of singularities of integrals and their integrands. Our results apply to any integral of Euler-Mellin type, and thus especially to every scalar Feynman integral. Specifically we provide for both the…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
A wide class of non-autonomous nonlinear parabolic partial differential equations with delay is studied. We allow in our investigations different types of delays such as constant, time-dependent, state-dependent (both discrete and…
We have studied the angular time delay in slow-electron elastic scattering by spherical targets as well as the average time delay of electrons in this process. It is demonstrated how the angular time delay is connected to the…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.