Stability for weighted composition $C_0$-semigroups on Lebesgue and Sobolev spaces
Javier Aroza, Elisabetta Mangino
TL;DR
This paper investigates the stability of weighted composition $C_0$-semigroups on Lebesgue and Sobolev spaces without relying on spectral conditions, and explores applications and hypercyclicity comparisons.
Contribution
It provides new stability criteria for weighted composition semigroups on Lebesgue and Sobolev spaces independent of spectral assumptions.
Findings
Established stability conditions without spectral analysis
Applied results to the generalized von Foerster-Lasota semigroup
Compared stability with hypercyclicity conditions
Abstract
Stability of weighted composition strongly continuous semigroups acting on Lebesgue and Sobolev spaces is studied, without the use of spectral conditions on the generator of the semigroup. Applications to the generalized von Foerster - Lasota semigroup and a comparison with hypercylicity conditions are presented.\
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Functional Equations Stability Results · Nonlinear Partial Differential Equations