Sentence examples for extends to a solution 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.

The only question relevant to the issue of constraints is whether an arbitrary state on an arbitrary spatial surface S can always be embedded into a space-time such that that state on S consistently extends to a solution on the entire space-time.

We show that the results in [8] are still true in hyperbolic background geometry setting, that is, the solution to Chow Luo's combinatorial Ricci flow can always be extended to a solution that exists for all time, furthermore, the extended solution converges exponentially fast if and only if there exists a metric with zero curvature.

In a minimal binary constraint network, every tuple of a constraint relation can be extended to a solution.

In the physics literature the following question has been asked: for any point p in T, and any space-like surface S that includes p is there a neighborhood E of p in S such that any solution on E can be extended to a solution on the whole space-time?

We further prove that the solution to Ge Xu's α-flow can always be extended to a solution that exists for all time and converges exponentially fast to constant α-curvature.

But whether the local solution can be extended to a global solution is a challenging open problem in the mathematical fluid mechanics.

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).