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

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...

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Published inNonlinear differential equations and applications Vol. 31; no. 2
Main Authors Fino, Ahmad Z., Ruzhansky, Michael, Torebek, Berikbol T.
Format Journal Article
LanguageEnglish
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
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-023-00907-2