Sentence examples for the initial data are from inspiring English sources

However, the initial data are Dirac-delta functions which are difficult to approximate numerically with a high accuracy.

Compared with that of [2], the minimal regularity index and the smallness assumptions we imposed on the initial data are weaker.

Since we may deal with the initial data in the weak Lp-spaces, the existence of self-similar solutions provided the initial data are small homogeneous functions.

We study the asymptotic behavior for large time of solutions to the Cauchy problem for the generalized Korteweg de Vries (gKdV) equationut+(|u|ρ−1 u)x+13uxxx=0, wherex, t∈Rwhen the initial data are small enough.

We study the regularizing properties of complex Monge Ampère flows on a Kähler manifold (X,ω) when the initial data are ω-psh functions with zero Lelong number at all points.

This behavior is especially important for employing a time-dependent approach to the steady state since the initial data are usually not known and a freestream condition or an intelligent guess for the initial conditions is often used.

Numerical tests show that the well-balanced method using an underlying numerical flux such as Lax Friedrichs flux, FORCE, GFORCE, or Roe fluxes can approximate very well the exact solution even when the initial data are on both supercritical region and subcritical region.

The initial data are impressive, yet the sample size is small.

Moreover, Problem (1.1) admits global solutions when the initial data are small (see [1]).

Suppose that for small the initial data are such that the norm is sufficiently small.

Finally, we show how small the initial data are for the global solutions to exist.