Related papers: Unitarity at small Bjorken x
We present an evolution equation for the Bjorken x dependence of diffractive dissociation on hadrons and nuclei at high energies. We extend the formulation of Kovchegov and Levin by relaxing the factorization assumption used there. The…
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage…
Polarised singlet DGLAP equations are solved by applying the method of characteristics. The singlet equations are first transformed into a pair of coupled partial differential equations by a Taylor series expansion valid to be at small x.…
In this paper the singlet and non-singlet structure functions have been obtained by solving Dokshitzer, Gribove, Lipatov, Alterelli, Parisi (DGLAP) evolution equations in leading order (LO) and next to leading order (NLO) at the small x…
In large but finite populations, weak demographic stochasticity due to random birth and death events can lead to population extinction. The process is analogous to the escaping problem of trapped particles under random forces. Methods…
We develop a new method to solve the Fokker-Planck or Kolmogorov's forward equation that governs the time evolution of the joint probability density function of a continuous-time stochastic nonlinear system. Numerical solution of this…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
In this paper the singlet and non-singlet hadron structure functions have been obtained by solving Dokshitzer-Gribov-Lipatov-Alterelli-Parisi (DGLAP) evolution equations in leading order (LO) at the small-x limit. Here we have used a Taylor…
We consider a stochastic logistic growth model involving both birth and death rates in the drift and diffusion coefficients for which extinction eventually occurs almost surely. The associated complete Fokker-Planck equation describing the…
Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. To this aim, we have developed an algorithm solving the radiative…
We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known…
We obtain the existence, uniqueness and regularity results for solutions to kinetic Fokker-Planck equations with bounded measurable coefficients in the presence of boundary conditions, including the inflow, diffuse reflection and specular…
As for the spatially homogeneous Boltzmann equation of Maxwellian molecules with the fractional Fokker-Planck diffusion term, we consider the Cauchy problem for its Fourier-transformed version, which can be viewed as a kinetic model for the…
In a previous work, a perturbative approach to a class of Fokker-Planck equations, which have constant diffusion coefficients and small time-dependent drift coefficients, was developed by exploiting the close connection between the…
This paper deals with the study of "\textit{sharp localized}" solutions of a nonlinear type Schr{\"o}dinger equation in the whole space $\R^N,$ $N\ge1,$ with a zero order term, in modulus, like a power $m$ less than one of the modulus of…
Known investigations of nonlinear evolution equations $${dx\over dt} + A(t)x(t) = f(t)\ ,\quad x(t_{0}) = x^{0},\ \quad t_{0} \le t < \infty\ , \eqno(0.1)$$ with monotone operators $A(t)$ acting from reflexive Banach space $B$ to dual space…
Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive…
We show that, for certain evolution partial differential equations, the solution on a finite interval $(0,\ell)$ can be reconstructed as a superposition of restrictions to $(0,\ell)$ of solutions to two associated partial differential…
A general framework is presented to discuss the approximate solutions of an evolution equation in a Banach space, with a linear part generating a semigroup and a sufficiently smooth nonlinear part. A theorem is presented, allowing to infer…
In this paper we investigate the stationary profiles of a nonlinear Fokker-Planck equation with small diffusion and nonlinear in- and outflow boundary conditions. We consider corridors with a bottleneck whose width has a global…