Initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary elliptic differential operator. (English) Zbl 1465.35387
Summary: An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the classical Fourier method. Sufficient conditions for the initial function and for the right-hand side of the equation are indicated, under which the corresponding Fourier series converge absolutely and uniformly. In the case of an initial-boundary value problem on \(N\)-dimensional torus, one can easily see that these conditions are not only sufficient, but also necessary.
MSC:
| 35R11 | Fractional partial differential equations |
| 35J40 | Boundary value problems for higher-order elliptic equations |
Keywords:
time-fractional subdiffusion equation; initial-boundary value problem; Fourier method; regular solution; Sobolev spacesReferences:
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