Generation of analytic semigroup for some generalized diffusion operators in Lp-spaces

TL;DR

This paper investigates the generation of analytic semigroups by certain fourth-order operators in Lp-spaces, using semigroup theory and functional calculus to analyze their spectral properties and invertibility.

Contribution

It demonstrates that specific fourth-order operators associated with five abstract Cauchy problems generate analytic semigroups in Lp-spaces, expanding understanding of their spectral behavior.

Findings

Operators generate analytic semigroups in Lp-spaces

Spectral properties are characterized using functional calculus

Invertibility conditions are established for the operators

Abstract

We consider five different abstract Cauchy problems where the operator is of fourth order. For each problem, using semigroups techniques and functional calculus, we study the invertibility and the spectral properties of the fourth order operator to show that it generates an analytic semigroup.