Blow-up phenomena for porous medium equation driven by the fractional p-sub-Laplacian
Jabbarkhanov K. Toleukhanov A.
2025American Institute of Mathematical Sciences
AIMS Mathematics
2025#10Issue 613498 - 13511 pp.
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.
blow-up solution , concavity method , fractional p-sub-Laplacian , fractional Poincaré inequality , fractional porous medium equation
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Institute of Mathematics and Mathematical Modeling, Pushkina, 125, Almaty, 050010, Kazakhstan
Satbayev University, Satpaev street 22a, Almaty, 050013, Kazakhstan
International School of Economics, Maqsut Narikbayev University, Korgalzhyn highway 8, Astana, 010000, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Satbayev University
International School of Economics
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