Sentence examples for existence of the initial from inspiring English sources

In evaluating the traction across the fluid-solid boundary, we need to consider the existence of the initial stress field.

The low temperature clustering could explain the existence of the initial phase, or modulated structure, seen experimentally at lower temperatures.

In Section 3 we study the existence of the initial value problem (1.1), while in Section 4 we deal with the initial value problem (1.2).

We first consider the existence of the initial value problem (IVP) of the evolution equation in E { u ′ ( t ) + A u ( t ) = f ( t, u ( t ) ), t > 0, u ( 0 ) = x 0. (5).

In particular, it is established that as a result of the existence of the initial twisting, at least in one constituent of the considered compound cylinder, the axisymmetric longitudinal and torsional waves cannot propagate separately, i.e. the new type axisymmetric waves, which differ from the axisymmetric torsional and longitudinal waves, must appear.

These theories allow a more accurate description of the diversity of Liesegang ring patterns [25], [34] and take into account the existence of the initial transient homogeneous colloidal state.

The ODE existence theorem yields the local unique existence of this initial value problem since the right hand side depends on (c_{i}) continuously.

The obtained results in Theorem 1 can be applied to the study of existence solutions of the initial Cauchy problem for singular linear systems of ordinary differential equations B ( t ) x ˙ = A ( t ) x + f ( t ), t ∈ [ a, b ], (18).

We are concerned with the existence of solutions of the initial value problem (1.1).

Recently, many researchers have given attention to the existence of solutions of the initial and boundary value problems for fractional differential equations.

The existence of an initial deformation decreased the amplitude difference of the beams that suffered from corrosion.