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Monotone traveling waves for delayed neural field equations
- Source :
- Mathematical Models and Methods in Applied Sciences, Mathematical Models and Methods in Applied Sciences, 2016, 26 (10), pp.1919-1954. ⟨10.1142/S0218202516500482⟩, Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2016, 26 (10), pp.1919-1954. ⟨10.1142/S0218202516500482⟩
- Publication Year :
- 2016
- Publisher :
- HAL CCSD, 2016.
-
Abstract
- International audience; We study the existence of traveling wave solutions and spreading properties for single-layer delayed neural field equations. We focus on the case where the kinetic dynamics are of monos-table type and characterize the invasion speeds as a function of the asymptotic decay of the connectivity kernel. More precisely, we show that for exponentially bounded kernels the minimal speed of traveling waves exists and coincides with the spreading speed, which further can be explicitly characterized under a KPP type condition. We also investigate the case of algebraically decaying kernels where we prove the non-existence of traveling wave solutions and show the level sets of the solutions eventually locate in between two exponential functions of time. The uniqueness of traveling waves modulo translation is also obtained.
- Subjects :
- Applied Mathematics
010102 general mathematics
Mathematical analysis
Function (mathematics)
Type (model theory)
01 natural sciences
Exponential function
010101 applied mathematics
Monotone polygon
Exponential growth
Modeling and Simulation
Kernel (statistics)
Bounded function
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Uniqueness
0101 mathematics
[MATH]Mathematics [math]
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 02182025 and 17936314
- Database :
- OpenAIRE
- Journal :
- Mathematical Models and Methods in Applied Sciences, Mathematical Models and Methods in Applied Sciences, 2016, 26 (10), pp.1919-1954. ⟨10.1142/S0218202516500482⟩, Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2016, 26 (10), pp.1919-1954. ⟨10.1142/S0218202516500482⟩
- Accession number :
- edsair.doi.dedup.....94db08ed428b126bf62364abfa6d7b19