The initial boundary value problem (2) makes it possible to describe, for example, the process of hydrogen corrosion, which is the diffusion of hydrogen into the structural material and, as a result, leading to a change in the properties of this material, as considered, for example, in [17].

mathematical models allowing to take into account possible emergent properties, can be presented in the form of related boundary and initial boundary value problems, each of which describes the particular processes occurring during the operation of NPP equipment;

it is of considerable interest to develop numerical methods for solving systems of coupled boundary and initial boundary value problems that combine differential equations of different types.

The first attempt in this direction is made in [12], where the initial boundary value problem for (BF) with the homogeneous Dirichlet boundary condition is studied and it is shown that this problem admits a unique global solution even for the 3-dimensional case.

In section 3 and 4, we give proofs of the main results for the initial boundary value problem and the periodic problem respectively.

In this subsection, we are going to prove the uniqueness of the solution of the initial boundary value problem for (BF).

Luchko,

Initial boundary value problems for the one dimensional time-fractional diffusion equation, Frac.

Initial boundary value problems for almost linear systems for unknown functions of two independent variables were considered in [16].

Functional differential inequalities of parabolic type and uniqueness results for initial boundary value problems were treated in [12], [13] and [15], [16].

We consider initial problems for functional differential equations of the Hamilton-Jacobi type and initial boundary value problems of the Dirichlet type for parabolic functional differential equations.

Leis,

Initial Boundary Value Problems in Mathematical Physics, John Wiley & Sons, New York, NY, USA, 1986.