Degenerate Time-dependent Variational Inequalities with Applications to Traffic Equilibrium Problems

2006 ◽  
Vol 6 (2) ◽  
pp. 117-133 ◽  
Author(s):  
A. Barbagallo
Keyword(s):  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Time Dependent ◽  
Traffic Network ◽  
Traffic Equilibrium ◽  
Monotone Variational Inequalities ◽  
Continuity Result ◽  
Traffic Equilibrium Problems ◽  
Network Equilibrium Problem ◽  
Discretization Procedure

Abstract The aim of this paper is to study the continuity of the solutions to degenerate time-dependent variational inequalities. In order to obtain the continuity of the solution, a previous continuity result for strongly monotone variational inequalities and an appropriate use of the convergence set in Mosco’s sense play an important role. The continuity result allows us to provide a discretization procedure for the calculation of the solution to the variational inequality which expresses the time-dependent traffic network equilibrium problem.

scholarly journals REGULARITY RESULTS FOR TIME-DEPENDENT VARIATIONAL AND QUASI-VARIATIONAL INEQUALITIES AND APPLICATION TO THE CALCULATION OF DYNAMIC TRAFFIC NETWORK

2007 ◽  
Vol 17 (02) ◽  
pp. 277-304 ◽  
Author(s):  
ANNAMARIA BARBAGALLO
Keyword(s):  
Variational Inequalities ◽  
Time Dependent ◽  
Network Equilibrium ◽  
Traffic Network ◽  
Set Convergence ◽  
Appropriate Use ◽  
Continuity Of Solutions ◽  
Regularity Results ◽  
Network Equilibrium Problem ◽  
Discretization Procedure

The aim of this paper is to consider time-dependent variational and quasi-variational inequalities and to study under which assumptions the continuity of solutions with respect to time can be ensured. Making an appropriate use of the set convergence in Mosco's sense, we are able to prove continuity results for strongly monotone variational and quasi-variational inequalities. The continuity results allow us to provide a discretization procedure for the calculation of solutions to the variational inequalities and, as a consequence, we can solve the time-dependent traffic network equilibrium problem.

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