The study of parabolic spectral fractional Laplacian with nonhomogeneous Dirichlet boundary conditions

Xingyu Liu; Xingyu Liu

doi:10.3934/math.20251094

AIMS Mathematics

2025, Volume 10, Issue 10: 24691-24711. doi: 10.3934/math.20251094

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The study of parabolic spectral fractional Laplacian with nonhomogeneous Dirichlet boundary conditions

Xingyu Liu ^,

The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen 518057, China

Received: 11 August 2025 Revised: 18 October 2025 Accepted: 22 October 2025 Published: 28 October 2025
MSC : 35R11, 26A33, 47A75, 35P05

We use characterizations of spectral fractional Laplacian to tackle the problems of parabolic spectral fractional Laplacian incorporating nonhomogeneous Dirichlet boundary conditions. Compared with applying classical extension method in the study of the lower-order fractional operators with $ s \in (0, 1) $, we used a modified extensions to parabolic spectral fractional Laplacian incorporating boundary conditions, adapted from constructing harmonic extensions of the boundary data to spectral fractional Laplacian.
- modified spectral fractional Laplace operator,
- nonzero boundary conditions,
- weak solution
Citation: Xingyu Liu. The study of parabolic spectral fractional Laplacian with nonhomogeneous Dirichlet boundary conditions[J]. AIMS Mathematics, 2025, 10(10): 24691-24711. doi: 10.3934/math.20251094

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Abstract

We use characterizations of spectral fractional Laplacian to tackle the problems of parabolic spectral fractional Laplacian incorporating nonhomogeneous Dirichlet boundary conditions. Compared with applying classical extension method in the study of the lower-order fractional operators with $ s \in (0, 1) $, we used a modified extensions to parabolic spectral fractional Laplacian incorporating boundary conditions, adapted from constructing harmonic extensions of the boundary data to spectral fractional Laplacian.

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