Sentence examples for super solution from inspiring English sources

A vector function defined on, for some, is called a sub (or super) solution of ( 1.1 )–( 1.3 ), if all the following hold: (1) ; (2) for, and for almost all ; (3) (2.1)  .

They're keen to emphasize their merits—stating they work with some of the most powerful tools on the planet, create new software, hardware, and super solutions that no one has ever heard of.

Since ∂Ω satisfies the Wiener criterion, we use the sub-super solution method similarly to [4] and get that the positive solution (u_{0}) of (1.2) is continuous up to ∂Ω.

Similarly, (u_{infty}(x)) is a super-solution to (3.6).

So z is a super-solution of problem (4.1).

Therefore, u ¯ is a super-solution of problem (1.1).

Proof We will prove this theorem by constructing a proper super-solution.

Then, ((overline{u}(t),overline{v}(t))) is a super-solution of (1.6).

Then it can be verified that v ( x, t ) is a super-solution of (1.1).

Here, we construct some super-solution to the problem, which is bounded for any (T>0).

Since u ̲ is a super-solution of (4.7), ϕ cannot exist globally.