Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation schemes by interacting...
CONTENTS1. Introduction.......................................................................................................................................................................... 52. Preliminaries....................................................................................................................................................................... 63. Random vector measures...................................................................................................................................................
We study asymptotic behavior of solutions to multifractal Burgers-type equation , where the operator A is a linear combination of fractional powers of the second derivative and f is a polynomial nonlinearity. Such equations appear in continuum mechanics as models with fractal diffusion. The results include decay rates of the -norms, 1 ≤ p ≤ ∞, of solutions as time tends to infinity, as well as determination of two successive terms of the asymptotic expansion of solutions.
In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous -norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.
Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·f(u) = 0, analyzing their -decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.
Semantic memory retrieval is one of the most fundamental cognitive functions in humans. It is not fully understood and researchers from various fields of science struggle to find a model that would correlate well with experimental results and help understanding the complex background processes involved. To study such a phenomenon we need a relevant experimental protocol which can isolate the basic cognitive functions of interest from other perturbations. A variety of existing medical tests can provide...
The 1994 Major League Baseball (MLB) Season ended prematurely when the players went on strike on August 12th, due to a labor disagreement with team owners. This paper describes the model estimation for predicting the runs scored in each of the unplayed games and gives the results of 1,000 simulations. Of particular interest are the Cleveland Indians and the Montreal Expos. The Expos were on pace to have the best season in franchise history (and the best record in the league), while the Indians were...
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