A direct discontinuous Galerkin method for a time-fractional diffusion equation with a Robin boundary condition

2019 ◽  
Vol 135 ◽  
pp. 15-29 ◽  
Author(s):  
Chaobao Huang ◽  
Martin Stynes
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Robin Boundary Condition ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Time Fractional Diffusion Equation ◽  
Robin Boundary

scholarly journals Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Jukka Kemppainen
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Diffusion Equation ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Robin Boundary Condition ◽  
Fractional Diffusion ◽  
Uniqueness Of The Solution ◽  
Time Fractional Diffusion Equation ◽  
Robin Boundary

Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition on a bounded domain with Lyapunov boundary is proved in the space of continuous functions up to boundary. Since a Green matrix of the problem is known, we may seek the solution as the linear combination of the single-layer potential, the volume potential, and the Poisson integral. Then the original problem may be reduced to a Volterra integral equation of the second kind associated with a compact operator. Classical analysis may be employed to show that the corresponding integral equation has a unique solution if the boundary data is continuous, the initial data is continuously differentiable, and the source term is Hölder continuous in the spatial variable. This in turn proves that the original problem has a unique solution.

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