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Multidimensional stability of V-shaped traveling fronts in time periodic bistable reaction–diffusion equations
- Source :
- Computers & Mathematics with Applications, Computers & Mathematics with Applications, 2016, 72 (6), pp.1714-1726. ⟨10.1016/j.camwa.2016.07.035⟩, Computers & Mathematics with Applications, Elsevier, 2016, 72 (6), pp.1714-1726. ⟨10.1016/j.camwa.2016.07.035⟩
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
Abstract
- International audience; This paper deals with the multidimensional stability of time periodic V-shaped traveling fronts in bistable reaction–diffusion equations. It is well known that time periodic V-shaped traveling fronts are asymptotically stable in two dimensional space. In the current study, we further show that such fronts are asymptotically stable under spatially decaying initial perturbations in Rn with n≥3. In particular, we show that the fronts are algebraically stable if the initial perturbations belong to L1 in a certain sense. Furthermore, we prove that there exists a solution oscillating permanently between two time periodic V-shaped traveling fronts, which implies that time periodic V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Finally we show that time periodic V-shaped traveling fronts are only time global solutions of the Cauchy problem if the initial perturbations lie between two time periodic V-shaped traveling fronts.
- Subjects :
- Current (mathematics)
Bistability
010102 general mathematics
Mathematical analysis
Time periodic V-shaped traveling fronts
01 natural sciences
Stability (probability)
010101 applied mathematics
Bistable
Computational Mathematics
Computational Theory and Mathematics
Two-dimensional space
Reaction diffusion equations
Modeling and Simulation
Stability theory
Bounded function
Reaction–diffusion system
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Initial value problem
0101 mathematics
Nonlinear Sciences::Pattern Formation and Solitons
Multidimensional stability
Mathematics
Subjects
Details
- ISSN :
- 08981221
- Volume :
- 72
- Database :
- OpenAIRE
- Journal :
- Computers & Mathematics with Applications
- Accession number :
- edsair.doi.dedup.....fc86203fc05a4ed0bde18bfffec2ecbd