Large time behaviour for the heat equation on Z, moments and decay rates

Abadias, Luciano (Universidad de Zaragoza) ; González-Camus, J. ; Miana, Pedro José (Universidad de Zaragoza) ; Pozo, J.C.

Resumen: The paper is devoted to understand the large time behaviour and decay of the solution of the discrete heat equation in the one dimensional mesh Z on lp spaces, and its analogies with the continuous-space case. We do a deep study of the moments of the discrete gaussian kernel (which is given in terms of Bessel functions), in particular the mass conservation principle; that is reflected on the large time behaviour of solutions. We prove asymptotic pointwise and lp decay results for the fundamental solution. We use that estimates to get rates on the lp decay and large time behaviour of solutions. For the l2 case, we get optimal decay by use of Fourier techniques.

Idioma: Inglés

DOI: 10.1016/j.jmaa.2021.125137

Año: 2021

Publicado en: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 500, 2 (2021), 125137 [25 pp]
ISSN: 0022-247X

Factor impacto JCR: 1.417 (2021)

Categ. JCR: MATHEMATICS rank: 77 / 333 = 0.231 (2021) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 127 / 267 = 0.476 (2021) - Q2 - T2

Factor impacto CITESCORE: 2.6 - Mathematics (Q2)

Factor impacto SCIMAGO: 0.859 - Applied Mathematics (Q1) - Analysis (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E26-17R
Financiación: info:eu-repo/grantAgreement/ES/MCYTS-MTM2016-77710-P
Financiación: info:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00
Financiación: info:eu-repo/grantAgreement/ES/UZ/JIUZ-2019-CIE-01

Tipo y forma: Article (Published version)

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