Work

Cazenave‐Dickstein‐Weissler‐Type Extension of Fujita'S Problem on Heisenberg Groups

Year: 2025

Type: article

Abstract: ABSTRACT This paper investigates the Fujita critical exponent for a heat equation with nonlinear memory posed on the Heisenberg groups. A sharp threshold is identified such that, for exponent values less than or equal to this critical value, no global solution exists, regardless of the choice of nonnegative initial data. Conversely, for exponent values above the threshold, global positive solutions exist under small initial data conditions. These findings extend the work of Cazenave, Dickstein, and Weissler, which addressed similar problems in the Euclidean setting. Furthermore, the paper provides lifespan estimates for local solutions under various initial data conditions. The analysis relies on the test function method and the Banach fixed‐point theorem to establish the main results.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70166

Authors: Mokhtar Kirane, Ahmad Z. Fino, Berikbol T. Torebek, Zineb Sabbagh

Institutions: Khalifa University of Science and Technology, American University of the Middle East, Ghent University, Institute of Mathematics and Mathematical Modeling, University of Blida

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $5,000

Funders: Universiteit Gent, Ministry of Education and Science of the Republic of Kazakhstan, Bijzonder Onderzoeksfonds UGent