About the Convergence of a Family of Initial Boundary Value Problems for\n a Fractional Diffusion Equation with Robin Conditions

2021/05/05 by Isolda Cardoso, Cardoso, Isolda, Sabrina Roscani +3
Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.2105.02122

Abstract

We consider a family of initial boundary value problems governed by a\nfractional diffusion equation with Caputo derivative in time, where the\nparameter is the Newton heat transfer coefficient linked to the Robin condition\non the boundary. For each problem we prove existence and uniqueness of solution\nby a Fourier approach. This will enable us to also prove the convergence of the\nfamily of solutions to the solution of the limit problem, which is obtained by\nreplacing the Robin boundary condition with a Dirichlet boundary condition.\n

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