A nonlinear hyperbolic system modeling currency hoarding. (English) Zbl 1421.35373
Summary: We present a nonlinear model for replacement, regulation of currency in circulation and hoarding currency. The nonlinearity enters the model in the regulatory term which depends on the total currency in the circulation. We provide an existence and uniqueness result for the model as well as its steady state. Local and global dynamics of the solution is studied for large time. In fact, convergence of the solution to the nontrivial steady state is obtained in both the linearized and nonlinear cases. Furthermore, we have analyzed the dynamics of the total currency in circulation and hoarding for large time by constructing a Lyapunov function. Convergence of the total currency in circulation and hoarding to the steady state is established using this Lyapunov function.
MSC:
| 35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |
| 91B55 | Economic dynamics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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