Sentence examples for considering the regularity from inspiring English sources

Considering the regularity of the problem, the asymptotic behavior of the two processes shall be the same, as we shall see in what follows.

Furthermore, considering the regularity of the level set function, we present an operator splitting method to update the level set function, which performs well in maintaining its smoothness and stability.

Then, considering the regularity of φ ̃ 1 in the region where φ ̃ 1 > 0, we can pass to the limit in the boundary condition for ( φ ^ 1 p 1 ) ξ 1 to obtain that - ( φ ̃ 1 p 1 ) ξ 1 ( 0 ) = φ ̃ 2 q 2 ( 0 ).

The relevance of considering the regularity of adolescents weighing or measuring practises and their opportunities for weighing and measuring themselves have previously been highlighted [ 7, 14].

In this paper, by employing tensor products of regularizing functions as in [7, 8], we consider the regularity of the solutions of (1.3) and prove in an elementary way that (1.3) can be reduced to the classical equation (1.1) of smooth functions.

We consider the regularity for weak solutions of second order nonlinear parabolic systems under controllable growth condition, and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point.

In this paper we consider the regularity of solutions to nonlinear Schrödinger equations (NLS), i ∂tu + 12 Δu = F u, u), (t, x) ∈ R × Rn,u(0) = φ, x ∈ Rn, where F is a polynomial of degree p with complex coefficients.

In this paper, we consider the regularity criteria for the 3D MHD equations.

The aim of this paper is to consider the regularity criterion; we will prove the following theorem.

We consider the regularity criterion to the density-dependent incompressible nematic liquid crystal model as follows [1 4]: div u = 0, (1.1).

For instance, Chae [5], Agélas [6], and Wu [7] considered the regularity of MHD equations, and Capone [8] and Fuchs [9] studied the stability bifurcation of MHD equations.