Dissipativity of semilinear time fractional subdiffusion equations and numerical approximations

The dissipativity with a bounded absorbing set in L2(Ω) for time-fractional nonlinear sub-diffusion equation is investigated. A numerical scheme based on the L1 method for time fractional derivative and the standard finite element method in space direction is presented. The proposed numerical scheme can preserve the dissipativity as the continuous equation. A numerical example is included to show the asymptotic behavior of the numerical method.