Fujita-type results for the degenerate parabolic equations on the Heisenberg groups
Fino A.Z. Ruzhansky M. Torebek B.T.
March 2024Birkhauser
Nonlinear Differential Equations and Applications
2024#31Issue 2
In this paper, we consider the Cauchy problem for the degenerate parabolic equations on the Heisenberg groups with power law non-linearities. We obtain Fujita-type critical exponents, which depend on the homogeneous dimension of the Heisenberg groups. The analysis includes the case of porous medium equations. Our proof approach is based on methods of nonlinear capacity estimates specifically adapted to the nature of the Heisenberg groups. We also use the Kaplan eigenfunctions method in combination with the Hopf-type lemma on the Heisenberg groups.
Critical exponents , Degenerate parabolic equation , Heisenberg group , Porous medium equation
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College of Engineering and Technology, American University of the Middle East, Egaila, 54200, Kuwait
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Institute of Mathematics and Mathematical Modeling, 125 Pushkin Str., Almaty, 050010, Kazakhstan
College of Engineering and Technology
Department of Mathematics: Analysis
School of Mathematical Sciences
Institute of Mathematics and Mathematical Modeling
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