Work

Non-autonomous semilinear fractional evolution equations: well-posedness and ultracontractivity results

Year: 2025

Type: article

Abstract: We consider a time-fractional semilinear parabolic abstract Cauchy problem for a time-dependent sectorial operator A ( t ) which satisfies the Acquistapace–Terreni conditions. We first prove local existence results for the mild solution of the problem at hand. Then we prove, under suitable assumptions on the initial datum, that the solution is also global in time. This is achieved by proving ultracontractivity estimates for the fractional evolution families associated with the operator A ( t ).

Source: Journal of Elliptic and Parabolic Equations

DOI: 10.1007/s41808-025-00422-8

Authors: Simone Creo, Maria Rosaria Lancia

Institution: Sapienza University of Rome

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni