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- 저자정보
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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.28 No.4
- 발행연도
- 2024.12
- 수록면
- 140 - 171 (32page)
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초록· 키워드
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We present the pathwise robustness of an instability phenomenon for the incoherent state to the kinetic Kuramoto-Fokker-Planck equation with random inputs in a large coupling regime. For the case in which coupling strength and initial fluctuation are deterministic, it is well known that the incoherent state is nonlinearly unstable by constructing an exponentially growing mode. In contrast, when uncertainties are present in the coupling strength and initial data, we show that the nonlinear fluctuations around the incoherent state exist globally and grow exponentially fast along the sample path as well. Thus, the instability phenomenon of the incoherent state is robust with respect to random inputs as long as the supports of natural frequency distribution are confined in a sufficiently small symmetric interval around zero.
목차
ABSTRACT
1. INTRODUCTION
2. PRELIMINARIES
3. PROPAGATION OF SOBOLEV REGULARITY FOR z-VARIATIONS
4. PATHWISE ROBUSTNESS OF INSTABILITY PHENOMENON I
5. PATHWISE ROBUSTNESS OF INSTABILITY PHENOMENON II
6. CONCLUSION
REFERENCES
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