Generalized Invariant Sets for the Boltzmann Equation

We are interested in the initial value problem for the Boltzmann equation, when the initial data u0 belongs to a set B0 = {δ0m1 (0,x,v) ≤ u0(x,v) ≤ C0m2 (0,x,v)} where m1, m2 are traveling Maxwellians. We consider soft or Maxwell's interactions with cutoff (7/3 < s ≤ 5) and C0 smaller than a bound depending on the coefficients of m2. We obtain global existence of solutions remaining in a "generalized invariant set" Bt ⊂ B∞, characterized by these particular states.

Download Full-text

Global existence of solutions of the Boltzmann equation for Bose–Einstein particles with anisotropic initial data

Journal of Functional Analysis ◽

10.1016/j.jfa.2018.09.010 ◽

2019 ◽

Vol 276 (1) ◽

pp. 231-283 ◽

Cited By ~ 3

Author(s):

Wenyi Li ◽

Xuguang Lu

Keyword(s):

Boltzmann Equation ◽

Initial Data ◽

Global Existence ◽

Existence Of Solutions ◽

Global Existence Of Solutions ◽

The Boltzmann Equation ◽

Bose Einstein

Download Full-text

Global existence of solutions for the relativistic Boltzmann equation with arbitrarily large initial data on a Bianchi Type I space-time

General Relativity and Gravitation ◽

10.1007/s10714-005-0179-8 ◽

2005 ◽

Vol 37 (12) ◽

pp. 2047-2062 ◽

Cited By ~ 12

Author(s):

Norbert Noutchegueme ◽

David Dongo ◽

Etienne Takou

Keyword(s):

Boltzmann Equation ◽

Initial Data ◽

Global Existence ◽

Bianchi Type ◽

Existence Of Solutions ◽

Type I ◽

Large Initial Data ◽

Bianchi Type I ◽

Relativistic Boltzmann Equation ◽

Global Existence Of Solutions

Download Full-text

Global existence of solutions for a multi-phase flow: A drop in a gas-tube

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891616500120 ◽

2016 ◽

Vol 13 (02) ◽

pp. 381-415

Author(s):

Debora Amadori ◽

Paolo Baiti ◽

Andrea Corli ◽

Edda Dal Santo

Keyword(s):

Global Existence ◽

Existence Of Solutions ◽

Inviscid Fluid ◽

Phase Flow ◽

Lagrangian Coordinates ◽

Large Initial Data ◽

Initial Value ◽

Global Existence Of Solutions ◽

Multi Phase Flow ◽

Multi Phase

In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main result concerns the global existence of weak entropic solutions to the initial-value problem for large initial data.

Download Full-text

Global existence of solutions for semilinear damped wave equations in R with noncompactly supported initial data

Nonlinear Analysis ◽

10.1016/j.na.2005.01.097 ◽

2005 ◽

Vol 61 (7) ◽

pp. 1189-1208 ◽

Cited By ~ 65

Author(s):

Ryo Ikehata ◽

Kensuke Tanizawa

Keyword(s):

Initial Data ◽

Global Existence ◽

Wave Equations ◽

Existence Of Solutions ◽

Global Existence Of Solutions

Download Full-text

Global Existence of Solutions for the Cauchy Problem of the Kawahara Equation with L 2 Initial Data

Acta Mathematica Sinica English Series ◽

10.1007/s10114-005-0710-6 ◽

2006 ◽

Vol 22 (5) ◽

pp. 1457-1466 ◽

Cited By ~ 55

Author(s):

Shang Bin Cui ◽

Dong Gao Deng ◽

Shuang Ping Tao

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Global Existence ◽

Existence Of Solutions ◽

Kawahara Equation ◽

Global Existence Of Solutions ◽

The Cauchy Problem

Download Full-text

Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data

Communications in Mathematical Physics ◽

10.1007/bf02099559 ◽

1996 ◽

Vol 176 (2) ◽

pp. 475-478 ◽

Cited By ~ 8

Author(s):

G. Rein ◽

A. D. Rendall

Keyword(s):

Initial Data ◽

Global Existence ◽

Existence Of Solutions ◽

Spherically Symmetric ◽

Small Initial Data ◽

Global Existence Of Solutions

Download Full-text

Global existence of solutions for the Einstein–Boltzmann system in a Bianchi type I spacetime for arbitrarily large initial data

Classical and Quantum Gravity ◽

10.1088/0264-9381/23/9/013 ◽

2006 ◽

Vol 23 (9) ◽

pp. 2979-3003 ◽

Cited By ~ 13

Author(s):

Norbert Noutchegueme ◽

David Dongo

Keyword(s):

Initial Data ◽

Global Existence ◽

Bianchi Type ◽

Existence Of Solutions ◽

Type I ◽

Large Initial Data ◽

Bianchi Type I ◽

Global Existence Of Solutions

Download Full-text

Local and global existence of solutions to semilinear parabolic initial value problems

Nonlinear Analysis ◽

10.1016/s0362-546x(99)00195-9 ◽

2001 ◽

Vol 43 (3) ◽

pp. 293-323 ◽

Cited By ~ 29

Author(s):

Shangbin Cui (Cui Shangbin)

Keyword(s):

Global Existence ◽

Initial Value Problems ◽

Existence Of Solutions ◽

Initial Value ◽

Global Existence Of Solutions ◽

Semilinear Parabolic

Download Full-text

Local and Global Existence of Solutions to Initial Value Problems of Modified Nonlinear Kawahara Equations

Acta Mathematica Sinica English Series ◽

10.1007/s10114-004-0446-8 ◽

2004 ◽

Vol 21 (5) ◽

pp. 1035-1044 ◽

Cited By ~ 9

Author(s):

Shuang Ping Tao ◽

Shang Bin Cui

Keyword(s):

Global Existence ◽

Initial Value Problems ◽

Existence Of Solutions ◽

Initial Value ◽

Global Existence Of Solutions

Download Full-text

Remarks on the critical nonlinear high-order heat equation

Arab Journal of Mathematical Sciences ◽

10.1016/j.ajmsc.2019.03.002 ◽

2019 ◽

Vol 26 (1/2) ◽

pp. 127-152

Author(s):

Tarek Saanouni

Keyword(s):

Global Existence ◽

Heat Equation ◽

Initial Value Problem ◽

Existence Of Solutions ◽

High Order ◽

Well Posedness ◽

Potential Well ◽

Initial Value ◽

Global Existence Of Solutions ◽

Nonlinear High Order

The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.

Download Full-text