Some remarks on the model of rigid heat conductor with memory: unbounded heat relaxation function
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