Sentence examples for maximum existence 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.

Fitting of titration curves in which the absorption maximum is plotted versus the ion concentration assumes the existence of two species with different maxima, with the intermediate maxima being proportional to the extent of interconversion between the species.

Results of existence, maximum principle and regularity of solutions are derived for these new variational inequalities.

Murray seems to have calibrated his real-world existence for maximum online appeal.

But, the existence of maximum or minimum solution will be failed.

Now, we state and prove the main theorem of this paper below, which provides the existence of maximum and minimum solutions to general variational inequalities in Hilbert lattices.