Sentence examples for by the weak solution from inspiring English sources

The purpose of incorporating a jet ejector into an absorption system is to improve the preabsorption of the refrigerant coming from the evaporator by the weak solution, i.e., to improve the overall absorption process.

The ejector has two functions: Firstly, it aids the pressure recovery from the evaporator and then upgrades the mixing process and pre-absorption by the weak solution of the methanol coming from the evaporator.

Moreover, the existence of pullback attractor for the 'partial-random' system generated by the weak solution is also presented.

The existence of the pullback attractor for the process generalized by the weak solution is presented in Section 5.

For the infinite-dimensional dynamical systems, Sell [5] constructed the semiflow generated by the weak solution which lacks the global regularity and obtained the existence of global attractor of the 3D incompressible Navier-Stokes equations on any bounded smooth domain.

For infinite-dimensional dynamical systems, Sell [21] constructed the semiflow generated by the weak solution which lacks the global regularity and obtained the existence of global attractor of the incompressible Navier-Stokes equations on any bounded smooth domain.

For every, by considering for each the weak solution to and by repeating the previous construction, we obtain a sequence which converges weakly in and strongly in to some with.

By the regularity theory, the weak solution is a classical solution.

Thus we have lim k → ∞ ∥ P + W k ∥ 2 = ∥ P + W ∥ 2, lim k → ∞ ∥ P − W k ∥ 2 = ∥ P − W ∥ 2. Thus lim k → ∞ ∥ W k ∥ = ∥ W ∥. and by (3.5), W is the weak solution of the equation W t t − W x x = 0 in  X.

Motivated by the desire to extend the weak solution results presented in Coclite and Karlsen [22], we consider Eq. (1) with its Cauchy problem in the form { u t − u t x x = − ∂ x ( m 2 u 2 ) + 3 u x u x x + u u x x x = − ( m 2 u 2 ) x + 1 2 ∂ x x x 3 u 2, u ( 0, x ) = u 0 ( x ), (5).

In the present work,we have used numerical scheme based on the definition of the weak solution given by [9].