Sentence examples similar to initial data state from inspiring English sources

Remark 1 It is easy to see that there is no blow-up solution for m = r = 1 in Theorem 4. Remark 2 The exact values of sufficiently large or small initial data stated in the theorems above will be given in the proofs of Section 3.

The continuous dependence of the solutions on initial data is stated in Theorem 2.1 below and is a straightforward consequence of Theorem 4.4 of [4].

Approximate controllability property is the possibility to steer the state of the system from any initial data to a state of arbitrary close to a target by choosing a suitable control.

Remark 2.2 The initial constraints (2.8) and (2.9) do not always require that the perturbation of the initial data around the equilibrium state ( ρ ¯, 0 ) is small.

Finally, we derive a sufficient condition of global existence of solutions to the Cauchy problem (1.1) by using the relation between initial data and the ground state solution of (1.4).

The corrected information shows a significant change for the North Carolina Tar Heels, who had no territory in the initial data and now dominate their state.

Hao [12] proved existence and uniqueness of global solutions for initial data close to some constant state in critical Besov space with minimal regularity.

We investigate the global existence and large time behavior of the solutions to the Cauchy problem of a multidimensional chemotaxis model with initial data close to a constant state.

This quasi-steady state (with initial data is taken from real kinematic experimental research) CFD study is based on flow simulation around swimmer's scanned hand models by using FLUENT (ANSYS, PA, USA).

Based on initial data supplied by the 50 states and the District of Columbia for the first six months of 2012, 25 states reported increases, 17 showed a decrease, and eight states and the District of Columbia reported no change.

For the numerical example, the MHD Riemann problem is used with the initial data consisting of two constant states lying to the right and to the left from the centerline of the computational domain.