Sentence examples for established provided that from inspiring English sources

Well-posedness of the transport properties is established, provided that some conditions on the kinetic data are met.

The existence and uniqueness of global weak solutions for Eq. (3) have been established provided that the initial data satisfy appropriate conditions in [6].

In [7, 29 33], the spacial decay rates for the strong solutions to the Camassa-Holm equation, the b-equation, and the Novikov equation were established provided that the corresponding initial data decay at infinity.

The spacial decay rates for the strong solutions to the Camassa-Holm and Novikov equations were established, provided that the corresponding initial datum decays at infinity [1, 45, 46].

In [38, 56, 57], the spatial decay rates for the strong solution to the Camassa-Holm Novikov equation were established provided that the corresponding initial datum decays at infinity.

We note that fully parabolic system of (1.2) was studied by [15] recently, and global existence and boundedness were established provided that the sensitivity function decays super linearly with respect to v. A bifurcation analysis is performed to establish nontrivial patterns.

The Constitution, and the structure of government that it established, provides the backdrop, but never the subject, for every controversy.

Collectively, this study demonstrates that plasma Pb measurements may be applied to general clinical settings, provided that established trace metal clean techniques are adopted.

The G-Fredholm property established earlier provides that the image of the Laplacian nontrivially intersects any closed, invariant subspace of L 2 (M ) of large enough dimension.

Until 1914 the established naval rules provided that warships could stop and search merchant vessels, but must safeguard their crews.

2485, established Dwight D. Eisenhower Leadership Program and provided that part D of former subchapter X of this chapter could be cited as the "Dwight D. Eisenhower Leadership Development Act of 1992".