Blow-up phenomena for porous medium equation driven by the fractional $ p $-sub-Laplacian

Khumoyun Jabbarkhanov; Amankeldy Toleukhanov; Khumoyun Jabbarkhanov; Amankeldy Toleukhanov

doi:10.3934/math.2025606

AIMS Mathematics

2025, Volume 10, Issue 6: 13498-13511. doi: 10.3934/math.2025606

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Blow-up phenomena for porous medium equation driven by the fractional $ p $-sub-Laplacian

Khumoyun Jabbarkhanov ^{1,3
,
,},
Amankeldy Toleukhanov ²

1.
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Pushkina, 125, Kazakhstan
2.
Satbayev University, Satpaev street 22a, Almaty 050013, Kazakhstan
3.
International School of Economics, Maqsut Narikbayev University, Korgalzhyn highway 8, Astana 010000, Kazakhstan

Received: 29 January 2025 Revised: 29 May 2025 Accepted: 03 June 2025 Published: 12 June 2025
MSC : Primary 35Q99; Secondary 35B44, 35A01, 35R11

In this paper, we investigate the global existence and blow-up phenomena of the solution to the fractional nonlinear porous medium equation on stratified groups, employing the concavity method. Specifically, we establish the necessary conditions for the existence of global solutions and blow-up solutions. Our findings not only contribute to the understanding of this equation on stratified groups but also extend the existing knowledge in the classical Euclidean setting to the fractional case.
- fractional porous medium equation,
- fractional Poincaré inequality,
- fractional $ p $-sub-Laplacian,
- concavity method,
- blow-up solution
Citation: Khumoyun Jabbarkhanov, Amankeldy Toleukhanov. Blow-up phenomena for porous medium equation driven by the fractional $ p $-sub-Laplacian[J]. AIMS Mathematics, 2025, 10(6): 13498-13511. doi: 10.3934/math.2025606

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Abstract

In this paper, we investigate the global existence and blow-up phenomena of the solution to the fractional nonlinear porous medium equation on stratified groups, employing the concavity method. Specifically, we establish the necessary conditions for the existence of global solutions and blow-up solutions. Our findings not only contribute to the understanding of this equation on stratified groups but also extend the existing knowledge in the classical Euclidean setting to the fractional case.

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