Sentence examples for the initial boundary from inspiring English sources

Consider the initial boundary value problem (1.3).

with the initial boundary conditions (3.2).

Figure 1 The computational domain and the initial boundary values.

We will study the initial boundary value problem of (1.2)–(1.5) in a bounded spatial domain (without loss of generality) with the initial-boundary data: (1.6).

This section deals with the study of the initial boundary value problem (1.3).

Consider the initial boundary value problem (3.1), and let the assumptions of Proposition 3.1 be satisfied.

to the initial boundary-value problem (1.1).

subject to the initial-boundary values (43).

The initial-boundary value problems are studied in [10, 11].

In this paper, we consider the initial-boundary value problem of one-dimensional compressible magnetohydrodynamics flows.

Finally, the exactness of the initial-boundary conditions guarantees that (xi^{0} = 0).