INVERSE SOURCE PROBLEM FOR A DEGENERATE SUBDIFFUSION EQUATION
Keywords:
time-fractional diffusion equation, degenerate equation, inverse problem, spectral methodAbstract
In the present paper, the inverse source problem is formulated and studied for a degenerate sub-diffusion equation in a rectangular domain. By employing the method of separation of variables, a spectral problem was obtained for an ordinary differential equation concerning the spatial variable. The existence of the eigenvalues and eigenfunctions of this spectral problem was established by equivalently reducing it to a homogeneous second-kind Fredholm integral equation with symmetric kernels. Using the theory of integral equations, the existence of the eigenvalues and eigenfunctions was further confirmed. The solution to the inverse source problem is expressed as the sum of a Fourier series over the system of eigenfunctions of the spectral problem. The uniform convergence of the obtained series of solution were proved.
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