Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity

Invasion entire solutions in a competition system with nonlocal dispersal

“…We only prove (38) and (40), since the proofs of (39) and (41) are similar to those of (38) and (40) (27), (28) and (30), we have…”

“…In Section 2, based on a fundamental theory (Proposition 1) which developed in [41] (see also [11]), we give the asymptotic behavior of traveling wave solutions at infinity. Section 3 is devoted to establishing the existence of invasion entire solutions by using comparison principle and constructing appropriate sub-super solution pairs.…”

“…To study the asymptotic behavior of solutions (φ, ϕ) of (9), we need the following result which is established by Zhang et al [41]. Lemma 2.2.…”

Traveling Wave Solutions in Nonlocal Dispersal Models With Nonlocal Delays

“…In literature, the corresponding propagation theory of nonlocal dispersal models (1.1) and (1.2) has been widely S. PAN studied, and most results are indexed by the traveling wave solutions and asymptotic speed of spreading. We refer to Bates et al [2], Carr and Chmaj [3], Chen [4], Coville and Dupaigne [5,6], Jin and Zhao [9], Li et al [10], Pan [14], Pan et al [15,16], Shen and Zhang [17], Sun et al [20], Wu and Liu [21], Xu and Weng [23], Zhang et al [26], Zhang et al [27] and the references therein.…”

Traveling waves for a nonlocal dispersal SIR model with delay and external supplies

“…[13,2,39,18]). Recently, traveling waves of nonlocal dispersal problems have attracted much attention, see for instance [29,22,45,2,6,5,[7][8][9]21,35,47] and references therein.…”