Similarly, (u_{infty}(x)) is a super-solution to (3.6).
Here, we construct some super-solution to the problem, which is bounded for any (T>0).
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.
Mr. Vranich, the author of "Super-Trains: Solutions to America's Transportation Gridlock" (St. Martin's Press, 1991), is not opposed to the Acela Express per se.
Beside, by incorporated with wireless charging techniques [18], the strong energy in synchronized carrier signaling may be used for remote powering, which may provide a feasible energy maintenance solution to super large-scale sensor networks.
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.
Both methods involve cooling a hot saturated lactose solution to super-saturation and then passing it through an orifice or applying mechanical agitation to initiate nucleation.
end{aligned}A function u is a weak super-solution (sub-solution) to (7.6) in E if whenever (Omega _{t_1,t_2} Subset E) for some domain (Omega subset mathcal {M}), we have (u in L^p(t_1,t_2;W^{1,p}(Omega ))), and the left hand side of (7.7) is non-negative (non-positive) for all non-negative test functions (W_0^{1,2}(t_1,t_2; L^2(Omega )) cap L^p (t_1,t_2; W_{Xi,0}^{1,p}(Omega ))).
This provides a solution to the "super-version" of the problem of Khamsi (1989).
The solution to problem (1.1) is a super-solution of (4.7).
