Sentence examples for be weak solutions of from inspiring English sources

Let ({u_{varepsilon}}) be weak solutions of (5).

Let ( u 1, q 1, z 1 ) and ( u 2, q 2, z 2 ) be weak solutions of the initial boundary value problem (2.9 - 2.17) in the sense of Definition  2.1 with given functions h 1 = h ( η ¯ 1 ), q in 1, q w 1, q out 1 and h 2 = h ( η ¯ 2 ), q in 2, q w 2, q out 2, respectively, and suppose that both h 1, h 2 satisfy (1.20).

Thus ({u_{n} }) are weak solutions of the problem (P).

The critical points of, that is, (3.2). for all, are weak solutions of problem (1.1).

Moreover, the critical points of J are weak solutions of (1.1).

Therefore, the critical points of φ are weak solutions of (P).

Furthermore, the critical points of J are weak solutions of problem (1).

Thus, the critical points of I in W are weak solutions of system (1.1).

(2.6) Consequently, the critical points of I are weak solutions of problem (1.1).

Moreover, the critical points of φ are weak solutions of (P).

Since, are weak solutions of the system we have that satisfies (3.30).