Existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation

2009 ◽  
Vol 33 (5) ◽  
pp. 563-575 ◽  
Author(s):  
Changming Song ◽  
Zhijian Yang
Keyword(s):  
Cauchy Problem ◽  
Global Solutions ◽  
Beam Equation ◽  
Nonlinear Beam ◽  
Existence And Nonexistence ◽  
The Cauchy Problem

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.

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