No abstract

This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of mild solutions for the abstract time-space evolution equation with delay under some quasimonotone conditions are obtained. Finally, the abstract results are applied to the time-space fractional delayed diffusion equation with fractional Laplacian operator, which improve and generalize the recent results of this issue.

In this paper, we are devoted to consider the periodic problem for the impulsive evolution equations with delay in Banach space. By using operator semigroups theory and fixed point theorem, we establish some new existence theorems of periodic mild solutions for the equations. In addition, with the aid of an integral inequality with impulsive and delay, we present essential conditions on the nonlinear and impulse functions to guarantee that the equations have an asymptotically stable ω-periodic mild solution.

The aim is to study the periodic solution problem for neutral evolution equa-in Banach space X, where A : D(A) ⊂ X → X is a closed linear operator, and −A generates a compact analytic operator semigroup T (t)(t ≥ 0). With the aid of the analytic operator semigroup theories and some fixed point theorems, we obtain the existence and uniqueness of periodic mild solution for neutral evolution equations. The regularity of periodic mild solution for evolution equation with delay is studied, and some the existence results of the classical and strong solutions are obtained. In the end, we give an example to illustrate the applicability of abstract results. Our works greatly improve and generalize the relevant results of existing literatures.

A Progressing Cavity Pump (PCP) works by forming a progressive seal cavity through the eccentric rotation of rotor. PCP parameters, such as eccentricity ratio [Formula: see text], can influence its performance and cavitation characteristics. The internal correlation among clearance fluid, cavitation characteristics, and pump performance should be explored to reveal the variation laws of internal flow and cavitation characteristics in PCP under different [Formula: see text]. In this study, a contrast analysis on external characteristics (e.g. volume efficiency) of pump with different eccentricity ratios was carried out by combining an RNG [Formula: see text] turbulence model based on Singhal full-cavitation model and the model pump test method. Moreover, gas volume distribution of PCP was analyzed and the optimal value range of eccentricity ratio was proposed. Results demonstrate that the axial force and axial power of PCP basically remain the same, volume efficiency increases, and cavitation performance decreases with the increase of [Formula: see text], and the optimal value for [Formula: see text] ranges from 0.17 to 0.24. In addition, a revised NPSHQ is proposed to quantify the cavitation characteristics of PCP.