101 research outputs found
Propagation of Delayed Lattice Differential Equations without Local Quasimonotonicity
This paper is concerned with the traveling wave solutions and asymptotic
spreading of delayed lattice differential equations without quasimonotonicity.
The spreading speed is obtained by constructing auxiliary equations and using
the theory of lattice differential equations without time delay. The minimal
wave speed of invasion traveling wave solutions is established by presenting
the existence and nonexistence of traveling wave solutions
Front-like entire solutions for monostable reaction-diffusion systems
This paper is concerned with front-like entire solutions for monostable
reactiondiffusion systems with cooperative and non-cooperative nonlinearities.
In the cooperative case, the existence and asymptotic behavior of spatially
independent solutions (SIS) are first proved. Combining a SIS and traveling
fronts with different wave speeds and directions, the existence and various
qualitative properties of entire solutions are then established using
comparison principle. In the non-cooperative case, we introduce two auxiliary
cooperative systems and establish some comparison arguments for the three
systems. The existence of entire solutions is then proved via the traveling
fronts and SIS of the auxiliary systems. Our results are applied to some
biological and epidemiological models. To the best of our knowledge, it is the
first work to study the entire solutions of non-cooperative reaction-diffusion
systems
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