Sentence examples for solution can be established from inspiring English sources
Apparently, the standard BEM cannot be applied to these problems, since no integral representation of the solution can be established.
In particular, the existence and uniqueness of the DUE solution can be established using the P-property of the Jacobian matrix.
Elasto-plastic, viscoplastic, and creep problems, however, are nonlinear, and this gives rise to a number of questions that must be resolved before a reliable solution can be established.
The relation between these two solutions can be established as the following theorem.
In particular, the transformation of the independent variable x described in Section 2.3 of CGK must be carried out before a criterion for oscillatory solutions can be established.
This underlines the need for transforming a given equation to the simplest possible form before a criterion for oscillatory solutions can be established.
In this section, the existence of strong solutions can be established by a standard argument, we construct the approximate solutions by using the iterative scheme, derive uniform bounds and thus obtain solutions of the original problem by passing to the limit.
This study has applied the analytical method to obtain the solutions to (MHD) in ℝ + 3. It proves that under the assumption that the initial data are close to the constant state, the global existence of smooth solutions can be established.
By a standard density argument, it is known that the same result can be established for strong solutions and for almost every t.
If the diffusion coefficient of the equation is degenerate on the boundary, no matter we can define the trace of the solution on the boundary or not, by choosing a suitable test function, the stability of the solutions always can be established without a boundary condition.
In the future, a natural question is whether the multiplicity of positive solutions for (1.1) can be established with negative exponent (frac{1}{u^{gamma}} (0<gamma<1)).
