Entire solutions in nonlocal dispersal equations with bistable nonlinearity

By Yu-Juan Sun, Wan-Tong Li, Zhi-Cheng Wang. 2011

97 citations recorded by the source corpus.

Abstract We consider entire solutions of nonlocal dispersal equations with bistable nonlinearity in one-dimensional spatial domain. A two-dimensional manifold of entire solutions which behave as two traveling wave solutions coming from both directions is established by an increasing traveling wave front with nonzero wave speed. Furthermore, we show that such an entire solution is unique up to space–time translations and Liapunov stable. A key idea is to characterize the asymptotic behaviors of the solutions as t → − ∞ in terms of appropriate subsolutions and supersolutions. We have to emphasize that a lack of regularizing effect occurs.

Subfields: Applied Mathematics, Mathematical Physics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/f864fba59390b0b7b3857adc8f39d934bf781f05