Sentence examples for boundary value problem defined from inspiring English sources

An important part in our considerations takes the following Neumann boundary value problem defined by (1.9).

Then the original problem is reduced to a boundary value problem defined in a domain without any crack tips.

Furthermore, the function stands for the unique solution of the auxiliary Neumann boundary value problem defined in (1.9).

We proceed first to obtain the uniqueness of the solution of the mixed initial boundary value problem defined by (8), (6) and (7).

The same technique can be carried over for the boundary value problem defined by (2) and (3) with M ∈ ( 0, π 2 4 ).

In various papers, the existence of the solution to the mixed initial boundary value problem defined by (8), (6) and (7) is obtained by assuming some strong restrictions.

Using the BEM and the fixed point method, we can easily apply this algorithm to the Signorini boundary value problems defined in domains of arbitrary shape.

The classical numerical treatment of boundary value problems defined on infinite intervals is to replace the boundary conditions at infinity by suitable boundary conditions at a finite point, the so-called truncated boundary.

Lastly, the uniqueness is investigated in solutions of the initial mixed boundary value problems defined by the 2-D theory, and some of special cases are indicated in the theory.

Many authors (see for example [2] [10]) studied the asymptotic behavior, as ε tends to zero, of solutions of scalar boundary value problems defined in a domain Ω ε obtained by removing from Ω closed smoothed cubes well contained in Ω (the holes) of diameter r ≤ ε periodically distributed with period ε in R n.

The unbounded boundary value problems defining these phenomena are redefined over bounded domains using appropriate radiation operators over finite artificial boundaries.