The model of rigid linear heat conductor with memory is reconsidered focussing the interest on the heat relaxation function. Thus, the definitions of heat flux and thermal work are revised to understand where changes are required when the heat flux relaxation function $k$ is assumed to be unbounded at the initial time $t=0$. That is, it is represented by a regular integrable function, namely $k\in L^1(\R^+)$, but its time derivative is not integrable, that is $\dot k\notin L^1(\R^+)$. Notably, also under these relaxed assumptions on $k$, whenever the heat flux is the same also the related thermal work is the same. Thus, also in the case under investigation, the notion of equivalence is introduced and its physical relevance is pointed out.
Some remarks on the model of rigid heat conductor with memory: unbounded heat relaxation function / Carillo, Sandra. - In: EVOLUTION EQUATIONS AND CONTROL THEORY. - ISSN 2163-2480. - 8:1(2019), pp. 31-42. [10.3934/eect.2019002]
Some remarks on the model of rigid heat conductor with memory: unbounded heat relaxation function
Sandra Carillo
2019
Abstract
The model of rigid linear heat conductor with memory is reconsidered focussing the interest on the heat relaxation function. Thus, the definitions of heat flux and thermal work are revised to understand where changes are required when the heat flux relaxation function $k$ is assumed to be unbounded at the initial time $t=0$. That is, it is represented by a regular integrable function, namely $k\in L^1(\R^+)$, but its time derivative is not integrable, that is $\dot k\notin L^1(\R^+)$. Notably, also under these relaxed assumptions on $k$, whenever the heat flux is the same also the related thermal work is the same. Thus, also in the case under investigation, the notion of equivalence is introduced and its physical relevance is pointed out.File | Dimensione | Formato | |
---|---|---|---|
paper_EECT_2019_Sandra_2163-2480_2019_1_31.pdf
accesso aperto
Note: http://aimsciences.org/article/doi/10.3934/eect.2019002
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Creative commons
Dimensione
360.14 kB
Formato
Adobe PDF
|
360.14 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.