Semigroups generated in Lp-spaces by some dispersal process including semi-permeability conditions at the interface

TL;DR

This paper investigates an elliptic differential equation modeling dispersal in two habitats with semi-permeability, demonstrating that the associated operator generates an analytic semigroup in Lp-spaces, advancing understanding of population dynamics models.

Contribution

It establishes the generation of an analytic semigroup for a dispersal model with semi-permeability conditions using functional calculus techniques.

Findings

Operator generates an analytic semigroup in Lp-spaces

Results apply to population dispersal models with semi-permeability

Advances mathematical understanding of habitat interface conditions

Abstract

We study an elliptic differential equation set in two habitats under semi-permeability conditions at the interface. This equation describes some dispersal process in population dynamics. Using functional calculus and results in Lutz Weis [22] among others, we show that the associated space operator generates an analytic semigroup in Lp-spaces.