期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 53, 期 6, 页码 7081-7112出版社
SIAM PUBLICATIONS
DOI: 10.1137/20M1343014
关键词
excitable system; traveling pulse solution; singular limit; front; back; free boundary problem
资金
- Ministry of Science and Technology of Taiwan [MOST 105-2115-M-032-005-MY3, MOST 105-2811-M-032-007, MOST 106-2811-M-032-009, MOST 107-2811-M-032-502]
- JSPS KAKENHI [JP16KT0022, JP20H01816]
- Young Scholar Fellowship Program of the Ministry of Science and Technology (MOST) in Taiwan [MOST 107-2636-M-024-001, MOST 108-2636-M-009-009, MOST 109-2636-M-009-008]
This study investigates the global dynamics of a one-dimensional free boundary problem in the singular limit of a FitzHugh-Nagumo type reaction-diffusion system. By introducing the notion of symbolic dynamics, the asymptotic behaviors of solutions are classified into three categories: convergence to resting state, convergence to a series of traveling pulses, and convergence to a propagating wave consisting of multiple traveling pulses and fronts.
The FitzHugh-Nagumo system has been studied extensively for several decades. It has been shown numerically that pulses are generated to propagate and then some of the pulses are annihilated after collision. For the mathematical understanding of these complicated dynamics, we investigate the global dynamics of a one-dimensional free boundary problem in the singular limit of a FitzHugh-Nagumo type reaction-diffusion system. By introducing the notion of symbolic dynamics, we show that the asymptotic behaviors of solutions are classified into three categories: (i) the solution converges uniformly to the resting state; (ii) the solution converges to a series of traveling pulses propagating in either the same direction or both directions; and (iii) the solution converges to a propagating wave consisting of multiple traveling pulses and two traveling fronts propagating in both directions.
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