Sentence examples for solutions for the evolution from inspiring English sources

Second, we develop numerical solutions for the evolution of surface patterns that are consistent with the developed analytical method.

Analytical solutions for the evolution of the contaminant concentration and the influenced region of the contaminant cloud are obtained by combining both the hydraulic and the ecological effects.

Especially, the existence of periodic solutions for the evolution equations has been considered by several authors; see [1 14] and the references therein.

In [2, 3], Byszewski discussed the existence of strong and classical solutions for the evolution equation d u ( t ) d t + A u ( t ) = f ( t, u ( t ) ), t ∈ ( t 0, t 0 + a ] (3).

In [6 12], the authors discussed the existence of solutions for various nonlinear differential equations or partial differential equations by measures of noncompactness and fixed point theorems, whereas in [13 16], the authors investigated the existence of solutions for the evolution equations by the monotone iterative method.

An analytical solution for the evolution equations of the system will be obtained.

Moreover, an analytical solution for the evolution of the size distribution, appropriate to the conditions in this study, has been obtained (Kumaran, 1998).

In this case, a series of computational experiments has been conducted to find an approximate exponential solution for the evolution of nodes' beliefs over time.

In this paper, we discuss the existence and asymptotic stability of the time periodic solution for the evolution equation with multiple delays in a Hilbert space Hu′(t)+Au(t)="F t,u(t),u(t−τ1),…,u(t−τn)),t∈R, where A D A ⊂ H→His a positive definite selfadjoint operator, F R×Hn+1→H is a nonlinear mapping which is ω-periodic in t, and τ1,…2,τnτn are positive constants.

We also find a threshold for the existence of global in time solutions of the evolution equation for the MEMS in the form of either a heat or a damped wave equation.

Employing the monotone iterative method, without the assumption of lower and upper solutions, we present some new results on the existence of positive mild solutions for the abstract evolution equations of fractional order.