About the Convergence of a Family of Initial Boundary Value Problems for a Fractional Diffusion Equation with Robin Conditions
Isolda Cardoso, Sabrina D. Roscani, Domingo A. Tarzia
We consider a family of initial boundary value problems governed by a
fractional diffusion equation with Caputo derivative in time, where the
parameter is the Newton heat transfer coefficient linked to the Robin condition
on the boundary. For each problem we prove existence and uniqueness of solution
by a Fourier approach. This will enable us to also prove the convergence of the
family of solutions to the solution of the limit problem, which is obtained by
replacing the Robin boundary condition with a Dirichlet boundary condition.