Work

Semilinear damped wave equations with data from Sobolev spaces of negative order: the critical case in the Euclidean setting and in the Heisenberg space

Year: 2025

Type: article

Abstract: In this note, we prove the global existence of solutions to the semilinear damped wave equation with critical nonlinearity in low space dimension, under the assumption that the initial data are small in the energy space and that the initial data belong to some Sobolev space of negative order. The latter is also called vanishing condition. A similar result also applies to the damped wave equation in the Heisenberg group.

Source: Journal of Evolution Equations

DOI: 10.1007/s00028-025-01132-3

Author: Marcello D’Abbicco

Institution: University of Bari Aldo Moro

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni