Cazenave-Dickstein-Weissler-Type Extension of FujitaS Problem on Heisenberg Groups
Kirane M. Fino A.Z. Torebek B.T. Sabbagh Z.
30 January 2026John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2026#49Issue 2499 - 511 pp.
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.
critical exponents , Heisenberg group , semilinear parabolic equations
Text of the article Перейти на текст статьи
Department of Mathematics, Faculty of Arts and Science, Khalifa University, Abu Dhabi, United Arab Emirates
College of Engineering and Technology, American University of the Middle East, Kuwait
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics, University Saad Dahleb, Blida, Algeria
Department of Mathematics
College of Engineering and Technology
Department of Mathematics: Analysis
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026