Asymptotic Speeds of Spread for a Nonlocal Diffusion Equation

Spreading speeds for a class of non-local convolution differential equation

“…We also point out that there have been some works on the the existence of spreading speeds for some non-monotone integro-differential equations (see, e.g. [16,22,30,28,19]).…”

“…When g(•) is monotone increasing on [0, w] and in the meantime Γ(•) is monotone increasing on [0, g(w)], the following results can be deduced from [22,30]. (ii) If u 0 ∈ X ω with u 0 ≡ 0, then the solution of (5) satisfies…”

“…By the integral form (9), the existence and uniqueness of solutions of (5) can be obtained by standard arguments (cf. [30]).…”