Related papers: Initial conditions and evolution of off-diagonal d…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…
We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the…
The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised…
The Kwiecinski evolution of unintegrated parton distributions (UPDs) in the transverse-coordinate space is analyzed with the help of the Mellin transform. Numerical results are presented for the unintegrated pion distributions with a simple…
A review of the present knowledge on polarized parton distributions is given. The effects of perturbative evolution on these distributions are discussed qualitatively and a comparison of various recent parametrizations is made.
Convolutions of long-tailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and showing…
We consider an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…
We use two-dimensional QCD as a toy laboratory to study off-forward parton distributions (OFPDs) in a covariant field theory. Exact expressions (to leading order in $1/N_C$) are presented for OFPDs in this model and are evaluated for some…
We reconsider the evolution equations for transverse momentum dependent distributions recently proposed by us and recast them in a form which allows the comparison with results recently appeared in the literature. We show under which…
A simple model of species origin resulted from dynamic features of a population, solely, is developed. The model is based on the evolution optimality in space distribution, and the selection is gone over the mobility. Some biological issues…
We propose a geometrically motivated mathematical model which reveals the key features of coastal and fluvial fragment shape evolution from the earliest stages of the abrasion. Our \textit{collisional polygon model} governs the evolution…
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting…
With unprecedented advances in genetic engineering we are starting to see progressively more original examples of synthetic life. As such organisms become more common it is desirable to be able to distinguish between natural and artificial…
The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for $H^s$ initial data, $s>-1/2$, and for any $s_1<\min(3s+1,s+1)$, the difference of the nonlinear and linear evolutions is in $H^{s_1}$…
We report on studies of multi-parton corrections from nonlocal operator expansion. We discuss relations between eikonal-line matrix elements and parton distributions, and present an illustration for initial-state collinear evolution.
The $Q^2$ evolution of polarised parton distributions at small $x$ is studied. Various analytic approximations are critically discussed. We compare the full evolution with that obtained from the leading-pole approximation to the splitting…
Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in…
We study the small-$x$ asymptotics of unpolarized generalized parton distributions (GPDs) and generalized transverse momentum distributions (GTMDs). Unlike the previous works in the literature, we consider the case of non-zero (but small)…
Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the…