Space and time estimates of second gradient thermal problems

doi:10.1007/s10483-025-3266-9

Applied Mathematics and Mechanics (English Edition) ›› 2025, Vol. 46 ›› Issue (7): 1403-1416.doi: https://doi.org/10.1007/s10483-025-3266-9

• • 上一篇

收稿日期:2025-02-14 修回日期:2025-05-09 发布日期:2025-06-30

Space and time estimates of second gradient thermal problems

J. R. FERNÁNDEZ¹^,^†(), V. PATA², R. QUINTANILLA³

^1.Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI Telecomunicación Campus As Lagoas Marcosende s/n, Vigo 36310, Spain
^2.Dipartamento di Matematica, Politecnico di Milano Piazza Leonardo da Vinci 32, Milano 20133, Italy
^3.Departamento de Matemáticas, E.S.E.I.A.A.T.-U.P.C., Terrassa 08222, Barcelona, Spain

Received:2025-02-14 Revised:2025-05-09 Published:2025-06-30
Contact: J. R. FERNáNDEZ E-mail:jose.fernandez@uvigo.es

摘要/Abstract

Abstract:

We consider the space and time decays of certain problems within the second gradient thermal law. Notably, for this thermal theory, the exponential time decay is precluded. First, the time estimates of polynomial type are obtained for both the thermal equation and the one-dimensional thermoelastic system, where the impossibility of localization with respect to time is also established. Then, the space estimates are deduced for the multidimensional thermoelastic problem, which allow to show the exponential decay of the energy.

Key words: second gradient theory, thermoelasticity, spatial estimate, polynomial decay

中图分类号:

O317

. [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(7): 1403-1416.

J. R. FERNÁNDEZ, V. PATA, R. QUINTANILLA. Space and time estimates of second gradient thermal problems[J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(7): 1403-1416.

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Space and time estimates of second gradient thermal problems

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