Sentence examples for behavior of a solution from inspiring English sources
The study of long-term behavior of a solution generated by dynamics on time scales always gains a great amount of attentions both from Engineers and from mathematicians.
For the behavior of a solution, generated by a nonmonotone initial function there are two possibilities: either is eventually monotone and, consequently, asymptotically convergent, or is eventually nonmonotone.
This is translated into an analysis of the large-time behavior of a solution to an age-structured time-dependent model.
Now, before solving ISDE (4.8), let us solve a crisp problem corresponding to (4.8), to investigate the behavior of a solution.
The asymptotic behavior of a solution and the research of using a degenerate solution to approximate the exact solution provide a theoretical basis for constructing the numerical simulation of the semiconductor devices.
To consider the behavior of a solution of different values of α, we will take advantage of the explicit formula Eq. (69) available for 0 < α ≤ 1 and consider the following three special cases.
The thermal behavior of a solution-cast liquid crystalline polymer (LCP) film was extensively studied by positron-annihilation lifetime spectroscopy (PALS).
To consider the behaviors of a solution for different values of α, we will take advantage of Eq. (15) available for 0 < α ≤ 1.
Based on the construction of this Green's function and by using perturbation arguments, we will answer the questions of existence, uniqueness and global behavior of a positive solution u in C 2 − α ( [ 0, 1 ] ) to problem (1.4), where C 2 − α ( [ 0, 1 ] ) is the set of all functions f such that x → x 2 − α f ( x ) is continuous on [ 0, 1 ].
Then we have the global existence and time-asymptotical behavior of a strong solution as follows.
Commonsensically, the behavior of a polymer solution would probably be affected by the spin coating rate during the deposition onto the porous substrate of alumina template due to the changes of surface energy [16].
