No abstract

We consider a functional semilinear Rayleigh-Stokes equation involving fractional derivative. Our aim is to analyze some circumstances, in those the global solvability, and asymptotic behavior of solutions are addressed. By establishing a Halanay type inequality, we show the dissipativity and asymptotic stability of solutions to our problem. In addition, we prove the existence of a compact set of decay solutions by using local estimates and fixed point arguments.

No abstract

We study a class of semilinear nonlocal partial differential equations, which model different problems related to processes in materials with memory. Our aim is to derive sufficient conditions ensuring the global solvability, regularity, and convergence to equilibrium of solutions