THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS

In this work,we study the linearized Landau equation with soft potentials and show that the smooth solution to the Cauchy problem with initial datum in L^(2)(ℝ^(3))enjoys an analytic regularization effect,and that the evolution of the analytic radius is the same as the heat equations.

Analytic Smoothing Effect of the Time Variable for the Spatially Homogeneous Landau Equation

In this work,we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework.We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an L^(2)initial datum for positive time.So that the smoothing effect of the Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.

The analytic smoothing effect of solutions for the nonlinear spatially homogeneous Landau equation with hard potentials

In this work,we study the Cauchy problem of the nonlinear spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework.We prove that the solution to the Cauchy problem with the initial datum in L^(2)enjoys an analytic regularizing effect,and the evolution of the analytic radius is the same as that of heat equations.

Gelfand-Shilov Smoothing Effect for the Radially Symmetric SpatiallyHomogeneous Landau Equation under the Hard Potentialγ=2

Based on the spectral decomposition for the linear and nonlinear radially symmetric homogeneous non-cutoff Landau operators under the hard potentialγ=2 in perturbation framework,we prove the existence and Gelfand-Shilov smoothing effect for solution to the Cauchy problem of the symmetric homogenous Landau equation with small initial datum.

Approximate Inertial Manifold for a Class of the Kirchhoff Wave Equations with Nonlinear Strongly Damped Terms

This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the smoothing effect of the solution, we make efficient use of the analytic property of the semigroup generated by the principal operator of the equation in the phase space. Then we obtain the regularity of the global attractor and construct the approximate inertial manifold of the equation. Finally, we prove that arbitrary trajectory of the Kirchhoff wave equations goes into a small neighbourhood of the approximate inertial manifold after large time.

Application of Sequential Indicator Simulation in Geological Study of X Oilfield in Zhujiangkou Basin

Sequential indicator simulation is a commonly used method for discrete variable simulation in 3D geological modeling and a widely used stochastic simulation method, which can be used not only for continuous variable simulation but also for discrete variable simulation. In this paper, the X Oilfield in the western South China Sea is taken as an example to compare the sequential indicator simulation method and the Indicator Kriging interpolation method. The results of the final comparison show that the results of the lithofacies model established by the Indicator Kriging deterministic interpolation method are overly smooth, and its coincidence rate with the geological statistical results is not high, thus cannot well reflect the heterogeneity of the underground reservoir, while the simulation results of the lithofacies model established by the sequential indicator stochastic simulation method can fit well with the statistical law of the well, which has eliminated the smoothing effect of Kriging interpolation, thus can better reflect the heterogeneity of the underground reservoir. Therefore, the sequential indicator simulation is more suitable for the characterization of sand bodies and the study of reservoir heterogeneity.

Initial Exploration of Wind Farm Cluster Hierarchical Coordinated Dispatch Based on Virtual Power Generator Concept

China has made many strides in large-scale development and centralized integration of wind power in recent years.The wind power penetration of some regions has reached a high level,which brings significant challenges for power system dispatch due to the inherent variability and uncertainty of wind resources.To increase the dispatch capabilities of wind power generation,the spatial smoothing effect among adjacent wind farms needs to be fully utilized.This paper presents the concept of hierarchical coordinated dispatch for wind power based on a new concept of a virtual power generator.The spatial smoothing effect of wind power is analyzed first.Next,the virtual power generator method of a wind farm cluster is defined and established.Then,the hierarchical coordinated dispatch mode is compared with an existing wind power dispatch mode for individual wind farms.Finally,the proposed concept is implemented on a simulation case to demonstrate applicability and effectiveness.