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Main Author:	Pawlak, Karolina
Format:	Preprint
Published:	2025
Subjects:	Analysis of PDEs 35R11, 47G40, 35R37
Online Access:	https://arxiv.org/abs/2506.15356
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author	Pawlak, Karolina
author_facet	Pawlak, Karolina
contents	This paper investigates the boundary behaviour of potential-type integrals for the multi-term time-fractional diffusion equation (MTFDE) across the moving boundary. First, we establish the jump relation for the integral operator associated with the fundamental solution of the inhomogeneous MTFDE. Second, we prove the continuity of the integral operator generated by the kernel corresponding to the homogeneous MTFDE. Krasnoschok obtained similar results for the time-fractional diffusion equation. However, in the multi-term case, the fundamental solution has more complex structure and does not admit standard scaling properties, which requires a different approach. Our results are essential for the analysis of boundary integral equations related to the MTFDE in time-dependent domains.
format	Preprint
id	arxiv_https___arxiv_org_abs_2506_15356
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Boundary behaviour of potential-type integrals for the multi-term time-fractional diffusion equation Pawlak, Karolina Analysis of PDEs 35R11, 47G40, 35R37 This paper investigates the boundary behaviour of potential-type integrals for the multi-term time-fractional diffusion equation (MTFDE) across the moving boundary. First, we establish the jump relation for the integral operator associated with the fundamental solution of the inhomogeneous MTFDE. Second, we prove the continuity of the integral operator generated by the kernel corresponding to the homogeneous MTFDE. Krasnoschok obtained similar results for the time-fractional diffusion equation. However, in the multi-term case, the fundamental solution has more complex structure and does not admit standard scaling properties, which requires a different approach. Our results are essential for the analysis of boundary integral equations related to the MTFDE in time-dependent domains.
title	Boundary behaviour of potential-type integrals for the multi-term time-fractional diffusion equation
topic	Analysis of PDEs 35R11, 47G40, 35R37
url	https://arxiv.org/abs/2506.15356

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