Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity

We study the diffusion equation in the absence of instantaneous elasticity $$ u_t-int_0^{t}g(t- au )Delta u( au ),d au =0,quad (x,t)in Omega imes (0,+infty ), $$ where $Omega subset mathbb{R}^n$, subjected to nonlinear boundary conditions. We prove that if the relaxation function g decays exponentially, then the solutions is exponential stable.