Differential games and nonlinear first order PDE on bounded domains

1984 ◽  
Vol 49 (2) ◽  
pp. 109-139 ◽  
Author(s):  
L. C. Evans ◽  
H. Ishii
Keyword(s):  
Differential Games ◽  
Bounded Domains ◽  
First Order ◽  
First Order Pde

scholarly journals Reduction of static field equation of Faddeev model to first order PDE

2007 ◽  
Vol 652 (5-6) ◽  
pp. 384-387 ◽  
Author(s):  
Minoru Hirayama ◽  
Chang-Guang Shi
Keyword(s):  
Field Equation ◽  
Static Field ◽  
First Order ◽  
First Order Pde ◽  
Faddeev Model

scholarly journals Mathematical analysis of nonlocal PDEs for network generation

2019 ◽  
Vol 14 (5) ◽  
pp. 506
Author(s):  
Tobias Böhle ◽  
Christian Kuehn
Keyword(s):  
Partial Differential Equations ◽  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Degree Distribution ◽  
Network Science ◽  
Steady States ◽  
Network Generation ◽  
First Order ◽  
First Order Pde ◽  
Implicit Ode

In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the degree distribution as time progresses. The evolution of the generating function of this degree distribution can be described by a nonlocal PDE. To address this equation we will rigorously convert it into a local first order PDE. Then, we use theory of characteristics to prove solvability and regularity of the solution. Next, we investigate the existence of steady states of the PDE. We show that this problem reduces to an implicit ODE, which we subsequently analyze. Finally, we perform numerical simulations, which show stability of the steady states.

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