Sentence examples for limit solutions from inspiring English sources

We prove that such limit solutions solve a free boundary problem of Hele Shaw type.

The brute-force approach contrasts drastically from examination of fine bifurcation structure of limit solutions of the system.

Notches and cracks are usually treated as two-dimensional problems in most structural design and analysis applications, employing 2D limit solutions from plane elasticity theories to evaluate highly localized stress/strain concentration effects around their tips.

In earlier works a kind of limit solutions x was considered (i.e. x is a limit of approximated solutions x n for problems driven by measures μ n tending, in some sense, to μ - cf. [52]).

If the initial transcription factor and morphogen patters are unimodal, we find two stable, non-zero stationary limit solutions.

Theoretically, the homogenized result corresponds to the limit solution when the size of the basic cell tends to be infinitely small.

A small displacement limit solution with an elastic-perfectly plastic material model overestimated the collapse load by more than 40% and could not reproduce the buckling behaviour.

Obviously, the limit solution ( p 0 e − i ( a t − 2 θ ), q 0 e − i ( a t − 2 θ ), b 0 ) is an exact plane-wave solution of (1.1).

From (1.12) and (1.13), we obtain the degenerate solution on the interval ([0,T]), that is, bar{x}= textstylebegin{cases} bar{x}^(t), & 0leq tleqsigma, bar{x}^(t), & sigmaleq tleq T. end{cases} (1.14) In general, the right limit solution is not equal to the left limit solution at (t=sigma), i.e., bar{x}(sigma- =lim_{trightarrowsigma^bar {x}^(t)neq lim _{trightarrowsigma- =lim_{trightarrowsigma^bar

Note that Theorem 5, although being able to prove convergence of both sequences {x t } and {z t }, cannot guarantee that the limit solution is feasible, i.e., it satisfies A x t =z t.

This implies that the model has to exhibit a stable stationary limit solution, which resembles the steady state gene expression pattern that is observed at E10.5.