Sentence examples for order equations in from inspiring English sources

For fourth order equations in (mathbb{R}^{3}), it is difficult to employ a conforming element.

All these problems are described by single fourth order partial differential equations or coupled with second order equations in presence of membrane forces.

Lions [13] proved that there exists a unique viscosity solution for a general class of fully nonlinear second order equations in an infinite dimensional Hilbert space.

In this article, we will study the Riemann boundary value problem for a kind of inhomogeneous partial differential system of first order equations in (R^{4}) using the Clifford analysis approach.

Applications of the established results show that they can be used to research oscillation for fractional order equations in various time scales such as fractional order differential equations, fractional order difference equations, and so on.

This rewrite of the second order equilibrium equations of elasticity in a 3-dimensional space as first order equations in a 6-dimensional space is analogous to replacing the Laplace equation by the Riemann Cauchy equations.

We reduce the system (15) to one 2-nd order equation in a normal form.

The cascade system identification problem for this case corresponds to solving a second order equation in a least squares sense constraining the roots to be real.

In this case, the scavenging rate can be described by a first order equation in particles concentration and the experimental results are consistent with theoretical predictions based on the classical model of atmospheric scavenging.

Now, in this paper, we extend the results of [24] to third-order equations in Banach spaces.

It should also be noted that some questions of solvability of nonlocal problems for fractional-order equations in the one-dimensional case were studied in [42 44].