相关论文: Delay Equations of the Wheeler-Feynman Type
The purpose of this paper is to investigate the stabilization of a one-dimensional coupled wave equations with non smooth localized viscoelastic damping of Kelvin-Voigt type and localized time delay. Using a general criteria of…
We describe a variational approach to a notion of Hamiltonian delay equations. Our delay Hamiltonians are of product form. We consider several examples. For closed symplectically aspherical symplectic manifolds $(M,\omega)$ we prove that…
It is pointed out that the usual derivation of the well-known Maxwell electromagnetic equations holds only for a medium at rest. A way in which the equations may be modified for the case when the mean flow of the medium is steady and…
In this work, a subdiffusion equation with constant time delay $\tau$ is considered. First, the regularity of the solution to the considered problem is investigated, finding that its first-order time derivative exhibits singularity at…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
The electromagnetic two-body problem has \emph{neutral differential delay} equations of motion that, for generic boundary data, can have solutions with \emph{discontinuous} derivatives. If one wants to use these neutral differential delay…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.
A simple method has been introduced to furnish the equilibrium solution of the Wigner equation for all order of the quantum correction. This process builds up a recursion relation involving the coefficients of the different power of the…
We derive the Euler equations from quantum dynamics for a class of fermionic many-body systems. We make two types of assumptions. The first type are physical assumptions on the solution of the Euler equations for the given initial data. The…
A Feynman formula is a representation of a solution of an initial (or initial-boundary) value problem for an evolution equation (or, equivalently, a representation of the semigroup resolving the problem) by a limit of $n$-fold iterated…
This paper introduces a modeling framework that is suitable to resolve singularities of impact phenomena encountered in applications. The method involves an exact transformation that turns the continuum, often partial differential equation…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
It is proved that approximations which are obtained as solutions of the multiphase Whitham modulation equations stay close to solutions of the original equation on a natural time scale. The class of nonlinear wave equations chosen for the…
We study the linear stability of a circular orbit in a two-electron atom, with the inclusion of retardation and self-interaction effects. We calculate all the eigenvalues of the linear stability of the circular orbit, expanded up to third…
In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive implicit $\Psi$--Hilfer fractional differential equations with time delay. It is…
We present a Friedmann-Robertson-Walker (FRW) quantum cosmological model within the framework of Finslerian geometry. In this work, we consider a specific fluid. We obtain the corresponding Wheeler-DeWitt equation as the usual constraint…
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…
The known nonlinear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim -- Uehling -- Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann…