About the Convergence of a Family of Initial Boundary Value Problems for a Fractional Diffusion Equation with Robin Conditions
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Publication:6366907
DOI10.1016/J.AMC.2022.127375arXiv2105.02122WikidataQ113880703 ScholiaQ113880703MaRDI QIDQ6366907
S. Roscani, Domingo A. Tarzia, Isolda E. Cardoso
Publication date: 5 May 2021
Abstract: 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.
Fractional derivatives and integrals (26A33) Series solutions to PDEs (35C10) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for linear higher-order PDEs (35G10) Fractional partial differential equations (35R11)
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