A nonlocal logistic equation with nonlinear advection term - de Lima, Romildo N.; Duarte, Ronaldo C.; Souto, Marco A. S. (Topological Methods in Nonlinear Analysis, 2026)
In this paper, we study a nonlocal logistic equation with nonlinear advection term equationPp cases -Δ u+α(x)· abla (u^p) =(λ-_ΩK(x,y)u^γ(y)dy )u &in Ω, u=0 & on Ω, cases P_p equation where Ω^N, N≥1, is a bounded domain with smooth boundary, α(x)=(α_1(x),…,α_N(x)) is a flow satisfying suitable condition, γ> 0, p≥1, λ and KΩ×Ω→ is a nonnegative function with KL^∞(Ω×Ω) and verifying other conditions that will be detailed below. It is very important to note that, this equation is not the classic logistic equation due to the inclusion of the term α(x)· abla (u^p), moreover, the inclusion of the integral nonlocal term on the right-hand side makes the problem closer to a real world situation.