Sentence examples for the solution for system from inspiring English sources

Lemma 3.1 Let y be the solution for system (7a - 7d).

However, the wave-breaking of the solution for system (1) is determined only by the slope of the component ρ of solution definitely.

Hence, the solution for system (1.1) with initial value (1.2) is almost surely unique on the interval ([t_{0} - tau,T]).

where A = a 2 2 γ ( 1 − γ ) 2. Proof According to the existence and uniqueness of W p, loc 2, 1 ( Q y ) ∩ ( Q ¯ y ∖ { y = 0 } ), the solution for system (4.5) can be proved by a standard penalty method (see Friedman [25]).

We need to point out that in the Sobolev spaces (H^{s}(mathbb{R} times H^{s-1}(mathbb{R})) with (s>frac{3}{2}), the wave-breaking of the solution for system (1) only depends on the slope of the component u of the solution [6].

In this section, we will change from the solution of system (1.1) to finding a fixed point for a vector-valued mapping, and by using the vector-valued mapping fixed point analysis method, show the convergence of the approximation sequences of the solution for system (1.1) in an ordered product Banach space.

Thus the solutions for system (1.4) are bounded.

Therefore, it is interesting to study the blow-up criterion of the solutions for system (1.1).

In this section we concern ourselves with the boundedness character of the solutions for System (9).

In this section, we study the asymptotic behavior of the solutions for system (1.1 - 1.6 1.1 - 1.6

Thus all the solutions for system (4) are uniformly bounded with an ultimate bound.