Fujita-type results for the degenerate parabolic equations on the Heisenberg groups

• Published in: Nonlinear differential equations and applications Vol. 31; no. 2
• Main Authors: Fino, Ahmad Z., Ruzhansky, Michael, Torebek, Berikbol T.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2024; Springer Nature B.V
• Subjects: Analysis; Cauchy problems; Eigenvectors; Mathematical analysis; Mathematics; Mathematics and Statistics; Porous media; Porous medium equation; Heisenberg group; Degenerate parabolic equation; 35B33; Secondary 35K65; 35B53; Primary 35A01; 35R03; Critical exponents

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...