Sentence examples for limit of the solution from inspiring English sources

It is enough that the upstream limit of the solution is available.

Furthermore, we observe that as (varepsilonrightarrow0), the limit of the solution of (1.3) and (3.1) is the corresponding Riemann solution of (1.3) and (1.4).

This example shows the significance of the middle sum in (1.3), since only this term contributes to the limit of the solution of (1.1) in this case.

In addition, it is not difficult to find that (mathit{RP}(U_{l},U_{r})) is the limit of the solution of the initial value problem.

The FFCC laws consist of nondelay feedback terms, disturbances compensation terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint vector equations.

We study the limit of the solution of linear and semilinear second order PDEs of parabolic type, with rapidly oscillating periodic coefficients, singular drift, and singular coefficient of the zeroth order term.

Then a weak solution is obtained as the limit of the solutions of such problems.

The main novelty of our paper is that we prove the existence of the limit of the solutions of the above equations under much weaker conditions than (1.9).

Finally, we verify that the limit of the solutions is exactly the solution to the original BSDE, which completes the proof.

Moreover, we prove that the solution of the Signorini contact problem can be obtained as the limit of the solutions of the contact problem with normal compliance as the stiffness coefficient of the foundation converges to infinity.

Phase plane trajectories, resonance curves and stability limit of the solutions are obtained and compared with the results of numerical integration in order to examine the validity of the present analysis.