Sentence examples for derivative of solution from inspiring English sources

The integral jump condition (1.3) means that a sudden change of solution values and the derivative of solution values at impulse point t k depend on the area under the curves of x ′ ( t ) and x ( t ) between t = t k − δ k to t = t k − ε k and t = t k − τ k to t = t k − σ k, respectively.

An alternative would be to generalize only the part of the results related to the exponential stability in the metric and the related estimates of the norms of solutions in the case of exponential stability and in the case of the exponential stability being not guaranteed (omitting the case of exponential stability in the metric and estimates of the norm of a derivative of solution).

In this paper, we deal with the relationship between the small function and the derivative of solutions of higher order linear differential equations.

In this article, we discussed the stable XFEM for the second order elliptic equation with discontinuous coefficients and derivative of solutions, and it comes to the following conclusions.

In Section 4, we present the Nagumo-type condition that we use in our existence result to a priori bound the derivative of solutions.

Next, we consider the behavior of the derivatives of solution (u_{a}) as (rrightarrow0).

Next we have to obtain the estimates for the normal derivatives of solution.

Formulae for the derivatives of solutions of diffusion equations are derived which clearly exhibit, and allow estimation of, the equations′ smoothing properties.

We present a new derivation of upper bounds for the decay of higher order derivatives of solutions to the unforced Navier Stokes equations in Rn.

Moreover, estimates for fractional derivatives of solutions by mean of suitable linear and nonlinear potentials are also implied.

A stochastic simulation algorithm is presented to calculate parametric derivatives of solutions of a population balance equation.