Sentence examples for the existence time from inspiring English sources

Moreover, the existence time can be chosen as follows:, where.

Then the existence time of a global solution for problem (1.1 - 1.2 1.1 - 1.2ise.

Next, we shall derive lower semicontinuity of the existence time, provided the initial data is smooth enough.

The selected molecular devices for water reduction have a unique property to enhance the existence time of photoelectrons, such that the likelihood of generated electron pairs to produce a molecule of hydrogen is increased.

Since the pressure satisfies (1.12), it follows from the a priori estimates in Theorem 3.1 that the existence time of the solution (({w^,w^)) can be extended after (t> T^), which contradicts the maximality of (t=T^).

(1) Let u ( t ) be any solution of problem (1.1 - 1.3 1.1 - 1.3tial energy J ( u 0 ) = e and I ( u 0 ) > 0 or ∥ ∇ u 0 ∥ p = 0, T be the existence time of u ( t ).

Let (T^) be the maximal existence time of the solution u.

If, then (1.4) has a unique nonnegative solution, where is the maximal existence time of the solution.

From the maximum principle for parabolic equations [16], it is not hard to verify that for, where is the maximal existence time of the solution.

Let T ≥ 0 be the maximal existence time of the unique solution u ( x, t ) with initial data u 0 ( x ).

Let be the maximal existence time of the solution, and combin and linearly, that is,, it follows from (1.4) that (2.2).