Global Well‐Posedness and Stabilization of a Viscoelastic Porous–Elasticity System Avoiding the Second Spectrum

ABSTRACT This paper investigates a one‐dimensional dissipative porous–elasticity system that circumvents the detrimental effects of the second spectrum, as highlighted in recent work by Ramos et al. (Applied Mathematics Letters 101 (2020): 106061). We first establish the global well‐posedness of the system using the Faedo–Galërkin method. Subsequently, by employing multiplier techniques and analyzing the memory‐driven viscoelastic damping, we derive explicit exponential decay rates for the system's energy.