Sentence examples for maximum existence time from inspiring English sources

Let T 0 be the maximum existence time.

for the maximum existence time T, where T ∈ (0, ∞]. Our main blow-up result for the problem (1.2) with arbitrarily positive initial energy is stated as follows.

which implies that T is not the maximum existence time and thus the solution ( u, w, b ) can be extended beyond T by the standard arguments of continuation of local solutions.

where T is the maximum existence time of solutions u 1 and u 2 and c depends on ∥ u 1 ( 0, x ) ∥ H 1 ( R ) and ∥ u 2 ( 0, x ) ∥ H 1 ( R ).

Here D ⊂ R N ( N ≥ 1 ) is a bounded domain with a smooth boundary ∂D, D ¯ is the closure of D, q = | ∇ u | 2, n is the outer normal vector and T is the maximum existence time of u ( x, t ). a ( u ) b ( x ) c ( t ), f ( x, u, q, t ) and h ( x, t ) r ( u ) are nonlinear diffusion coefficient, reaction term and boundary flux, respectively.

Let u 0 ( x ) ∈ H s ( R n ) with s > n 2. Then the Cauchy problem (3) has a unique solution u ( t, x ) ∈ C ( [ 0, T ) ; H s ( R n ) ) ∩ C 1 ( [ 0, T ) ; H s − 1 ( R n ) ) where T is the maximum existence time. Moreover, lim t → T ∥ u ( t, ⋅ ) ∥ H s ( R n ) = ∞. if and only if lim t → T ∥ u ( t, ⋅ ) ∥ L ∞ ( R n ) = ∞. For the case of space dimension n = 1, we have the result.

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.

Summer's approaching and that means maximum beach time.

Read more: Judge Gives York University Rapist Maximum Prison Time.

HIIT should be done maximum one time per week with full recovery made before lifting again.

RMWT: recommended maximum waiting time.