Related papers: Evolution profiles and functional equations
In this paper, we investigate abstract time-fractional evolution equations with nonlinear perturbations. We construct solutions of Lipschitz perturbation problems in arbitrary large time interval independent of the Lipschitz constants. We…
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 consider evolution differential equations in Fr\'echet spaces that possess unconditional Schauder basis and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE and…
The aim of this paper is to study the evolution of a material point of a body by itself, and not the body as a whole. To do this, we construct a groupoid encoding all the intrinsic properties of the particle and its characteristic…
One can study communications by using Shannon's (1948) mathematical theory of communication. In social communications, however, the channels are not "fixed", but themselves subject to change. Communication systems change by communicating…
We obtain the renormalized equations of motion for matter and semi-classical gravity in an inhomogeneous space-time. We use the functional Schrodinger picture and a simple Gaussian approximation to analyze the time evolution of the…
Recently new solvable systems of nonlinear evolution equations -- including ODEs, PDEs and systems with discrete time -- have been introduced. These findings are based on certain convenient formulas expressing the $k$-th time-derivative of…
By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the…
This paper establishes new estimates for linear Schroedinger equations in R^3 with time-dependent potentials. Some of the results are new even in the time-independent case and all are shown to hold for potentials in scaling-critical,…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…
We consider functional differential equations(FDEs) which are perturbations of smooth ordinary differential equations(ODEs). The FDE can involve multiple state-dependent delays or distributed delays (forward or backward). We show that,…
We construct the time-evolution for the second quantized Dirac equation subject to a smooth, compactly supported, time dependent electromagnetic potential and identify the degrees of freedom involved. Earlier works on this (e.g.…
We study stochastic evolution equations describing the dynamics of open quantum systems. First, using resolvent approximations, we obtain a sufficient condition for regularity of solutions to linear stochastic Schroedinger equations driven…
Fluctuation and dissipation dynamics is examined at all temperature ranges for the general case of a background time evolving scalar field coupled to heavy intermediate quantum fields which in turn are coupled to light quantum fields. The…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
We consider the evolution of a population of fixed size with no selection. The number of generations $G$ to reach the first common ancestor evolves in time. This evolution can be described by a simple Markov process which allows one to…
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
The time evolution of the universe is usually mathematically described under a continuous time and thus time reversible. Here, the consequences of studying the evolution of a homogenous isotropic universe by time continuous reversible…