Time-step heat problem on the mesh: asymptotic behaviour and decay rates

Abadías Ullod, Luciano (Universidad de Zaragoza) ; González-Camus, Jorge ; Rueda, Silvia

Resumen: In this article, we study the asymptotic behavior and decay of the solution of the fully discrete heat problem. We show basic properties of its solutions, such as the mass conservation principle and their moments, and we compare them to the known ones for the continuous analogue problems. We present the fundamental solution, which is given in terms of spherical harmonics, and we state pointwise and ℓp estimates for that. Such considerations allow to prove decay and large-time behavior results for the solutions of the fully discrete heat problem, giving the corresponding rates of convergence on ℓp spaces.

Idioma: Inglés

DOI: 10.1515/forum-2022-0334

Año: 2023

Publicado en: FORUM MATHEMATICUM 35, 6 (2023), [20 pp.]
ISSN: 0933-7741

Factor impacto JCR: 1.0 (2023)

Categ. JCR: MATHEMATICS rank: 117 / 489 = 0.239 (2023) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 181 / 331 = 0.547 (2023) - Q3 - T2

Factor impacto CITESCORE: 1.6 - Mathematics (all) (Q2) - Applied Mathematics (Q3)

Factor impacto SCIMAGO: 0.692 - Mathematics (miscellaneous) (Q1) - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E26-17R
Financiación: info:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00
Financiación: info:eu-repo/grantAgreement/ES/UZ/JIUZ-2019-CIE-01

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)