| Autor: |
XU-DONG ZHAO, WAN-TONG LI, MING-ZHEN XIN |
| Zdroj: |
SIAM Journal on Applied Mathematics; 2024, Vol. 84 Issue 5, p2087-2109, 23p |
| Abstrakt: |
This paper focuses on the existence, nonexistence, and stability of generalized transition waves for neural field equations in time heterogeneous media. Roughly speaking, we prove that generalized transition waves exist for any sufficiently large wave speed function in the sense of the least mean value, while such solutions do not exist for wave speed functions with small least mean value. We also show that generalized transition waves are asymptotically stable when they exist, indicating that they attract those solutions whose initial values decay as fast as generalized transition waves near infinity and essentially above zero near negative infinity. Our approach is based on the construction of lower-upper solutions and limit argument, in which we give some new Lipschitz regularity estimates for the solutions of some Cauchy problems to overcome the difficulties caused by the time-dependent nonlinear nonlocal term. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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