Sentence examples for maximum principle it from inspiring English sources

According to strong maximum principle, it follows that.

Futhermore, by the weak maximum principle it follows that u ≥ 0 in Ω.

From the maximum principle it follows that v x,t) ≤ 0, ∀ x ∈ [0,1], ∀ t > 0.▀.

By the maximum principle, it follows that u ( x, t ) ≥ 0 in the time interval of existence.

Hence, on the basis of the maximum principle, it follows that the solution of system (2.6 - 2.8 2.6 - 2.8nd it is uniquexists [11]).

First, thanks to the maximum principle, it follows from (1.1) and (1.3) that Vert theta Vert _{L^{infty}(0,T L^{infty})}leq C. (3.1).

By applying the maximum principle [24], it follows from (2.18) that P can attain its nonnegative maximum only for D ¯ × { 0 } or ∂ D × ( 0, T ).

Pontryagin's Maximum Principle makes it possible to account for related closure constraints together with interaction efforts at cut joints in a quite general and efficient way in stating and solving the dynamic optimization problem.

If (lambda<0) or (lambda>alpha), by the maximum modulus principle, it is easy to see that (S_{alpha,lambda}) consists of constants.

Using the maximum modulus principle, it follows that for all ζ ∈ U ∗ and each t > 0, arbitrarily fixed, there exists θ = θ ( t ) ∈ R such that | H ( ζ, t ) | < max | ζ | = 1 | H ( ζ, t ) | = | H ( e i θ, t ) | (3.12).

Combining (2.19 - 2.21) and applying maximum principles [23], it follows that the minimum of Ψ in (overline{D}times[0,T)) is zero. Thus, we have Psigeq0 quad mbox{in } overline{D}times[0,T), that is, the differential inequality frac{g' u)}{{mathrm{e}}^{u}}u_{t}geqbeta. (2.22) Suppose that (x_{0}inoverline{D}) and (u_{0}(x_{0})=M_{0}).