Sentence examples for coefficient case from inspiring English sources

The condition c 3 = 0 implies that g ( t ) = g ¯ 0 and h ( t ) = h ¯ 0 which corresponds to a constant coefficient case.

We then bootstrap these estimates to obtain optimal Strichartz and maximal function estimates, all of which turn out to be identical to the constant coefficient case.

As before, it is useful to consider a new dimensionless variable (tilde {x}), this time chosen to make the coefficients of Eq. (32) more similar to those of the constant coefficient case.

Analogous estimates in the (L^p) spaces, for operators independent of (epsilon ) are well known (see for instance [76] for the constant coefficient case and [9] for the Carnot group setting).

We extend to the variable coefficient case boundary layer techniques that have been successful in the treatment of the Laplace equation and certain other constant coefficient elliptic partial differential equations on Lipschitz domains in Euclidean space.

In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

Among the works mentioned, we notice that most of the current research on numerical methods for solving FDEs are concerned with the constant-coefficient case, and relatively less attention has been paid to the cases with variable coefficient.

Two-grid analysis for the linear constant-coefficient case shows that it is difficult to obtain uniformly good convergence rates for a higher-order scheme, because of waves perpendicular to stream lines.

Laine and Yang [12] considered the entire functions coefficients case and got the following.

In addition to the degeneracy and self-sharpening of the GPME with continuous coefficients, detailed in [1], increased numerical challenges occur in the discontinuous coefficients case.

Bank and Laine [12] have shown that the number of zeros of a solution should also be taken into account in the meromorphic coefficients case.