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math.AP2026
Logistic elliptic and parabolic problem for the fractional -Laplacian
Loïc Constantin, Carlos Alberto Santos, Guillaume Warnault
In this paper we prove existence, uniqueness of weak solutions of the following nonlocal nonlinear logistic equation \begin{equation*} \begin{cases} (-Î)_p^s u_λ=λu_λ^q - b(x)u…
math.AP2025
Modelling Capillary Rise with a Slip Boundary Condition: Well-posedness and Long-time Dynamics of Solutions to Washburn's Equation
Isidora RapajiÄ, Srboljub SimiÄ, Endre Süli
The aim of this paper is to extend Washburn's capillary rise equation by incorporating a slip condition at the pipe wall. The governing equation is derived using fundamental princi…