Sentence examples for extends to a solution of from inspiring English sources

then u extends to a solution of the A-Dirac equation in Ω.

then u extends to a solution of the A-Dirac system in Ω.

then extends to a solution of the A-Dirac equation in.

We show that for anyt∈R, the maph→ξt(h) is continuous in thep-variation topology for anyp⩾1, so that it uniquely extends to a solution flow on the space of all geometric rough paths.

Conversely, every continuous function f 0 : I ( x 0, f 0 ( x 0 ) ) → R such that (2.12) is satisfied and (2.11) holds for all x, y ∈ I ( x 0, f 0 ( x 0 ) ) can be uniquely extended to a continuous solution f : ( 0, + ∞ ) → ( 0, + ∞ ) of equation (1.1).

This contributing solution was extended to a study of the capability of DORIS to dynamically estimate the variation in the geocentre location.

The proposed optimization approaches can be extended to the solution of integer programming problems in other engineering disciplines also.

The vorticity-velocity formulation of the Navier-Stokes equations is extended to the solution of three-dimensional compressible fluid flow and heat transfer problems.

These methods are further extended to the solution of the quasi-linear PDE given by (1 - 2).

By adding a certain penalty term to the Black-Scholes equation, the solution of this variational inequality is extended to a fixed domain.

This work presents results on the boundary properties of solutions of a complex, planar, smooth vector field L. Classical results in the Hp theory of holomorphic functions of one variable are extended to the solutions of a class of nonelliptic complex vector fields.