Sentence examples for between the weak solution from inspiring English sources
The device serves two major functions: it facilitates pressure recovery and improves the mixing process between the weak solution and the refrigerant vapor coming from the evaporator.
The device served two major functions: it facilitated pressure recovery and improved the mixing between the weak solution and the refrigerant vapour coming from the evaporator.
First, we consider the distance between the weak solution u of (1) and the nth multilevel solution (u_{n}in S_{n}) obtained by the wavelets of order p. Theorem 4.1 in [13] stated that, for (uin H_{0}^{1}(varOmega ) cap H^{s} varOmega ) ), there exists a positive constant C such that |u-u_{n}| + 2^{-n}|u-u_{n}|_{1} leq C bigl(2^{-n} bigr)^{s}|u|_{s},quad 1leq sleq p+1.
Now it is well known that there is a one-to-one correspondence between the weak solutions of (1.1) and the critical points of I on (W^{1,p}_{0}(Omega)).
Now it is well known that there exists a one-to-one correspondence between the weak solutions of problem ( P 0 Q ) and the critical points of ℱ.
It is well known that there exists a one-to-one correspondence between the weak solutions of problem ( P 0 K ) and the critical points of ℰ.
Now it is well known that there exists a one-to-one correspondence between the weak solutions of problem (2.1) and the critical points of I on (W^{1,p}_{0}(Omega)).
By (2.1), (h.1), (h.2), and Lemma 4.1, we easily see that J h is well defined and of C 1. Thus there exists a one-to-one correspondence between the weak solutions of ( P h Q ¯ ) and the critical points of J h.
end{aligned} (4.2) It follows from (4.1) and (4.2) that (mathscr{E}_{sigma}inmathscr{C}^{1}((mathscr{D}_{G}^{2, 2}(mathbb{R}^{N}))^{2}, mathbb{R})) and there exists a one-to-one correspondence between the weak solutions of ((mathscr {P}_{sigma}^{overline{Q}})) and the critical points of (mathscr{E}_{sigma}).
Indeed, We know that the weak solution.
