Using the Frobenius series method (FSM), an analytical solution is developed to obtain mechanical stresses of thick spherical pressure vessels made of functionally graded materials (FGMs). The cylinder pressure vessel is subjected to uniform internal pressure. The modulus of elasticity is graded along the radial direction according to power functions of the radial direction. It is assumed that ...

Abstract We study parabolic equation with the tempered fractional Laplacian and logarithmic nonlinearity by direct method of moving planes. first prove several important theorems, such as asymptotic maximum principle, narrow region principle strong for antisymmetric functions, which are critical factors in process Then, we further derive some properties radial solution to a unit ball. These con...

Consider the energy critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let W be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, u...

This paper undertakes the problem of optimal shunt capacitor placement for loss reduction in a radial distribution feeder. The objective is to determine the optimum size and location of the capacitors to be placed on a radial distribution system. The objective function is to have maximization of saving due to reduction of energy losses thereby taking into consideration cost of capacitor. The so...

In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...

We investigate the focusing Ḣ-critical nonlinear Schrödinger equation (NLS) of Hartree type i∂tu + ∆u = −(| · |−3 ∗ |u|2)u with Ḣ radial data in dimension d = 5. It is proved that if the maximal life-span solution obeys supt ∥|∇| 12 u ∥∥ 2 < √ 6 3 ∥|∇| 12Q ∥∥ 2 , where Q is the positive radial solution to the elliptic equation with nonlocal operator (1.4) which corresponds to a new variational ...