Mathematical analysis reveals solution instability and conditional exponential decay in thermo-poroelastic systems, highlighting stability criteria for negative elastic regimes.
In this work, we study some qualitative properties of a one-dimensional thermo-poroelastic problem with microtemperatures when the elastic coefficient is negative. First, we obtain a result regarding the uniqueness and instability of solutions. Secondly, we restrict ourselves to the quasi-static case and we see that, if the inverse of the absolute value of the elastic coefficient is small in comparison with the heat capacity coefficient, then we can obtain the existence, uniqueness and exponential decay of the solutions.
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Fernández et al. (2025) studied this question.
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