Integral Kernel Estimates for a Linear Singular Operator Linked with Boltzmann Equation Part 2: Small Singularities 0 < Ν < 1 and Regularity Issues
نویسنده
چکیده
In this work, we continue the study of precise functional properties of a linear operator linked with Boltzmann quadratic operator, started in Part I. This is done for singular cross-sections. In particular, we show Calderon-Zygmund type estimates.
منابع مشابه
Integral Kernel Estimates for a Linear Singular Operator Linked with Boltzmann Equation Part I: Small Singularities 0 < Ν < 1 and Besov to L P Estimates
where the unknown f(t, x, v) is a nonnegative integrable function standing for the density of particles in phase space : time t ≥ 0, position x ∈ R, velocity v ∈ R, n ≥ 2. More precisely, this first part is devoted to some properties linked with the operator from (1.13) below, which is linked with one possible weak formulation of Boltzmann equation (1.1). On the right hand side of (1.1), Q is t...
متن کاملWavelet-based numerical method for solving fractional integro-differential equation with a weakly singular kernel
This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel. First, a collocation method based on Haar wavelets (HW), Legendre wavelet (LW), Chebyshev wavelets (CHW), second kind Chebyshev wavelets (SKCHW), Cos and Sin wavelets (CASW) and BPFs are presented f...
متن کاملA finite difference method for the smooth solution of linear Volterra integral equations
The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...
متن کاملA Revision on Classical Solutions to the Cauchy Boltzmann Problem for Soft Potentials
This short note complements the recent paper of the authors [2]. We revisit the results on propagation of regularity and stability using Lp estimates for the gain and loss collision operators which had the exponent range misstated for the loss operator. We show here the correct range of exponents. We require a Lebesgue’s exponent α > 1 in the angular part of the collision kernel in order to obt...
متن کاملJu l 2 00 6 Cooling process for inelastic Boltzmann equations for hard spheres , Part II : Self - similar solutions and tail behavior
We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar solutions, and we give pointwise estimates on their tail. We also give general estimates on the tail and the regularity of generic solutions. In particular we prove Haff's law on the rate of decay of t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005