Sentence examples for data of problem from inspiring English sources

In Section 3, we derive the condition on the data of problem (1.1) sufficient to guarantee the global existence of u ( x, t ).

We derive the conditions on the data of problem (1.1) sufficient to guarantee that blow-up will occur, and obtain an upper bound for t ∗.

Theorem 2 Let Ω be a bounded domain in R 3, and assume that the data of problem (1.1) satisfy conditions (3.4), (3.16), (3.17).

In respect of the data of problem (A), we also assume that A, B and F ∈ L p, 2 ( C ) and γ ∈ C α.

Theorem 3.2 Assume that the data of problem (CFP- α 1 ) satisfy the conditions (i), (ii), (iv - vi) of Theorem  3.1 and.

Let us stress that g j , as well as g j, do not depend on the choice of fundamental system u ˜ 1, …, u ˜ n, but only on the data of problem (6).

An optimization problem is said to be well posed if the solution of the problem uniquely exists and the solution depends continuously on the data of the problem.

Roughly speaking, Hadamard types of well-posedness for a problem means the continuous dependence of the optimal solution from the data of the problem.

Normally the data of the problem are state functions known with a given degree of precision and in solving this problem the precision can be enhanced.

On the other hand, exact solutions of the problems may not exist in many practical problems because the data of the problems are not sufficiently 'regular'regular

where the dependence of the constant C on the data of the problem is fully determined.