Direct methods for a dual tempered fractional parabolic problem
Guo, Yuxia (Tsinghua University (Pequin, Xina). Department of Mathematical Science)
Hu, Yichen (Dalian University of Technology (Dalian, Índia). School of Mathematical Sciences)
Peng, Shaolong (Beihang University (Pequin, Xina). School of Mathematical Sciences)

Date:	2026
Abstract:	In this paper, we consider the dual tempered fractional parabolic problema ∂ s t u(x, t) − (∆ + ρ) α 2 u(x, t) = f(t, u(x, t)), Ω × R, where Ω may be Rn or Rn + := {x ∈ Rn | x1 > 0}, s ∈ (0, 1), α ∈ (0, 2), and ρ is a sufficiently small positive constant. We prove that the positive solutions are strictly increasing in the x1 direction without assuming the solutions to be bounded. We will introduce two methods for dealing with the above dual tempered fractional parabolic problem: the method of moving planes and sliding methods. Unlike previous articles, we investigate the problems that involve both the fractional time derivative ∂ s t and the tempered fractional Laplacian −(∆ + ρ) α 2 . First, by establishing the narrow region principle and averaging effects for the dual tempered fractional parabolic operators ∂ s t −(∆+ αρ) 2 , and then developing the direct moving planes to derive the monotonicity of solutions for the dual tempered fractional parabolic problem in Rn + × R. Second, by establishing maximum principles in unbounded open sets for problems involving dual tempered fractional parabolic operators, we develop direct sliding methods for the tempered fractional parabolic problem, and derive the onedimensional symmetry of solutions to the dual tempered fractional parabolic problem in Rn × R. As applications, we also prove the Gibbons conjecture for entire solutions to the dual tempered fractional parabolic problem.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Dual tempered parabolic equations ; Fractional time diffusion ; Maximum principles ; Averaging effects ; Dire
Published in:	Publicacions matemàtiques, Vol. 70, Num. 2 (2026) , p. 549-585 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/1500000000000147
DOI: 10.5565/PUBLMAT7022610

37 p, 1.1 MB

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