Nonlocal Filtration Equations with Rough Kernels in the Heisenberg Group

2022/09/06 by Rong Tang, Tang, Rong
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2209.02181

openalex publication_date 2022/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by the extensive investigations of integro-differential equations on ℝⁿ, we consider nonlocal filtration type equations with rough kernels on the Heisenberg group ℍⁿ. We prove the existence and uniqueness of weak solutions corresponding to suitable initial data. Furthermore, we obtain the large time behavior of solutions and the uniform Hölder regularity of sign-changing solutions for the porous medium type equations (m≥ 1). Notice that both conformal fractional operators \mathscrL_α/2 and pure power fractional operators \mathscrL^α/2 on the Heisenberg group ℍⁿ have their integral representations with suitable kernels. Therefore, all the results in this paper will hold for these equations with operators \mathscrL_α/2 or \mathscrL^α/2.

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