Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 29, Issue 11, Pages 2063-2087Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202519500404
Keywords
The steady state; integro-differential equation; convergence rates
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Funding
- National Natural Science Foundation of China [11701557, 11701556]
- Foreign Expert Projects [BG20190001019, T2018060]
- Fundamental Research Funds for the Central Universities [2016QS01]
- National Science Foundation [DMS1812666]
- NSF Grant RNMS (Ki-Net) [1107444, 1107291]
- NSF [DMS 1614537, DMS 1908739]
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This paper is concerned with large time behavior of solutions to a semi-discrete model involving nonlinear competition that describes the evolution of a trait-structured population. Under some threshold assumptions, the steady solution is shown unique and strictly positive, and also globally stable. The exponential convergence rate to the steady state is also established. These results are consistent with the results in [P.-E. Jabin, H. L. Liu. Nonlinearity 30 (2017) 4220-4238] for the continuous model.
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