Sentence examples for persistence of the solution from inspiring English sources
In the previous section, we have investigated the persistence of the solution to model (9).
A result concerning the persistence of the solutions is provided prior to proving the main theorems.
The aim is to establish persistence properties of the solution flow in the weighted Sobolev spaces Zs,r="Hs(R)∩L2(|x|2rdx), s∈R, s⩾1 and s⩾r.
Recently, the well-posedness and persistence properties of the solution for (1.4) were established in [40 42].
Establish the persistence of the issue, what solutions have failed, and why.
We prove the existence, uniqueness, and persistence of the regularity for the solutions of this fluid-structure interaction problem.
In this paper, we mainly study persistence properties for a generalized Camassa-Holm equation with cubic nonlinearity, and we prove the persistence properties in weighted spaces of the solution to the equation, provided that the initial potential satisfies a certain sign condition.
The persistence properties of the strong solution were found.
Two results about the persistence properties of the strong solution for Eq. (1.2) were established in [7].
A corresponding result on persistence of strong solutions of the CH and Novikov equations and of Equation (1.1) can be found in [9, 45, 50], respectively.
The persistence of the problem has led to solutions ranging from simply building really big batteries to pumping underground caverns full of air to pushing a train full of rocks uphill.
