The Fujita exponent for a semilinear heat equation with forcing term on Heisenberg group
Borikhanov M.B. Ruzhansky M. Torebek B.T.
February 2025John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2025#48Issue 33794 - 3810 pp.
In this paper, we study a critical exponent to the semilinear heat equation with forcing term on Heisenberg group. Our technique of proof is based on methods of nonlinear capacity estimates specifically adapted to the nature of the Heisenberg group. The critical exponent will be bounded for all dimensions of the Heisenberg group, in contrast to the Euclidean case which in the 1D and 2D cases will be infinite. In addition, we give an upper bound estimate on the lifespan of local solutions.
blow-up and global solution , Heisenberg group , semilinear heat equation
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Khoja Akhmet Yassawi International Kazakh–Turkish University, Turkistan, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Khoja Akhmet Yassawi International Kazakh–Turkish University
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
School of Mathematical Sciences
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