scholarly journals Global solutions to the initial value problem for the nonlinear Boltzmann equation

1976 ◽  
Vol 12 (1) ◽  
pp. 229-239 ◽  
Author(s):  
Takaaki Nishida ◽  
Kazuo Imai
Keyword(s):  
Boltzmann Equation ◽  
Initial Value Problem ◽  
Global Solutions ◽  
Nonlinear Boltzmann Equation ◽  
Initial Value

scholarly journals Convergence of Global Solutions to the Cauchy Problem for the Replicator Equation in Spatial Economics

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Equilibrium Solution ◽  
Global Solutions ◽  
Initial Time ◽  
Spatial Economics ◽  
Replicator Equation ◽  
Unique Global Solution ◽  
Initial Value ◽  
The Cauchy Problem

We study the initial-value problem for the replicator equation of theN-region Core-Periphery model in spatial economics. The main result shows that if workers are sufficiently agglomerated in a region at the initial time, then the initial-value problem has a unique global solution that converges to the equilibrium solution expressed by full agglomeration in that region.

On the initial value problem for the Boltzmann equation with a force term

1989 ◽  
Vol 18 (1) ◽  
pp. 87-102 ◽  
Author(s):  
N. Bellomo ◽  
M. Lachowicz ◽  
A. Palczewski ◽  
G. Toscani
Keyword(s):  
Boltzmann Equation ◽  
Initial Value Problem ◽  
Force Term ◽  
Initial Value ◽  
The Boltzmann Equation

scholarly journals On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Hatice Taskesen ◽  
Necat Polat ◽  
Abdulkadir Ertaş
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Type Equation ◽  
Global Solutions ◽  
Initial Energy ◽  
Potential Well ◽  
Global Weak Solutions ◽  
Power Type ◽  
Initial Value ◽  
The Cauchy Problem

We will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity and supercritical initial energy. By defining new functionals and using potential well method, we readdressed the initial value problem of the Boussinesq-type equation for the supercritical initial energy case.

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