Longtime dynamics for a nonlinear viscoelastic equation with time-dependent memory kernel

Well‐posedness and exponential decay for the Moore–Gibson–Thompson equation with time‐dependent memory kernel

“…In the case of time-dependent memory, we refer the reader to Conti et al [26,27] (see also previous works [28][29][30]). In previous studies [26,27], the authors studied the equation arising in the theory of viscoelasticity…”

“…In the case of time‐dependent memory, we refer the reader to Conti et al [26, 27] (see also previous works [28–30]). In previous studies [26, 27], the authors studied the equation arising in the theory of viscoelasticity $$$$ {\partial}_{tt}u-\left(1+{k}_t(0)\right)\Delta u-{\int}_0^{\infty }{k}_t^{\prime }(s)\Delta u\left(t-s\right)\mathrm{d}s+f(u)=g, $$$$ where $$$ {k}_t\left(\cdotp \right) $$$ depends on time, $$$ f(u) $$$ is a nonlinear term and $$$ g=g(x) $$$ is an external force.…”