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Structure of positive radial solutions of Matukuma's equation
Springer Science and Business Media LLC - Tập 8 - Trang 165-173 - 1991
Eiji Yanagida
We study the structure of solutions of a semilinear elliptic equation called Matukuma's equation. This equation is a mathematical model for describing the dynamics of a globular cluster of stars. It is known that, under some conditions, there exists a solution called a positive entire solution with finite total mass. It is conjectured that the finite total mass solution is unique. In this paper th...... hiện toàn bộ
Numbers of equilibria for the equation of self-gravitating isentropic gas surrounding a solid ball
Springer Science and Business Media LLC - Tập 13 - Trang 311-331 - 1996
Wen-chi Kuan, Song-sun Lin
For self-gravitating, spherically symmetric and isentropic gas surrounding a solid star, when the adiabatic index γ ∈ [4/3, 2) we prove that there is a unique equilibrium for given momentum and total mass. When γ ∈ (1, 4/3), we prove that there are multiple equilibria for a certain range of momentum and total mass and the number of equilibria may grow arbitrarily larger for certain γ. These result...... hiện toàn bộ
On the numerical analysis of some variational problems with nonhomogeneous boundary conditions
Springer Science and Business Media LLC - Tập 15 - Trang 345-361 - 1998
M. Chipot, A. Elfanni
The goal of this note is to expose a new techniques to get energy estimates for nonconvex problems with nonlinear boundary conditions in term of the mesh size of a Lagrange finite elements method.
Some low order nonconforming mixed finite elements combined with Raviart–Thomas elements for a coupled Stokes–Darcy model
Springer Science and Business Media LLC - Tập 30 - Trang 565-584 - 2013
Peiqi Huang, Jinru Chen
In this paper, we discuss numerical methods to solve a coupled Stokes–Darcy system. The deformation tensor form of Stokes equations is used to describe the fluid flow motion. The mixed form of elliptic equation is applied to describe the porous media flow motion. We propose finite element methods for the coupled problem. For Stokes equations, one component of the velocity is approximated by Crouze...... hiện toàn bộ
A class of preconditioner for solving the Riesz distributed-order nonlinear space-fractional diffusion equations
Springer Science and Business Media LLC - Tập 40 - Trang 537-562 - 2022
Jian-Wei Yu, Chun-Hua Zhang, Xin Huang, Xiang Wang
In this paper, we study the fast algorithm for the numerical solution of the Riesz distributed-order nonlinear space-fractional diffusion equation. The finite difference method is employed to discretize the problem, the resulting system is symmetric positive definite Toeplitz matrix and then the fast Fourier transform can be used to reduce the computational cost of the matrix–vector multiplication...... hiện toàn bộ
Optimization of film-type optical fiber wiring design using mixed-integer programming problem
Springer Science and Business Media LLC - - Trang 1-25 - 2023
Hiroki Ishikura, Takashi Wakamatsu, Nozomi Hata, Katsuki Fujisawa
Optical fibers are among the most widely used tools in information communication today, and they have had an active development trajectory. Film interconnection is among the methods applied to optical fibers. However, due to its characteristics, the interconnection design must be done well so that each fiber satisfies several design requirements. In this study, we developed a mathematical model fo...... hiện toàn bộ
A reaction–diffusion approximation of a semilinear wave equation with damping
Springer Science and Business Media LLC - Tập 39 - Trang 921-941 - 2022
Hiroko Sekisaka-Yamamoto
A reaction–diffusion approximation is a method that solutions of multi-component reaction–diffusion systems approximate those of differential equations. We introduce the reaction–diffusion approximations of a semilinear wave equation and a semilinear damped wave equation under some assumptions of a reaction term. These approximation systems consist of a two-component reaction–diffusion system with...... hiện toàn bộ
Fairing of planar curves to log-aesthetic curves
Springer Science and Business Media LLC - Tập 40 - Trang 1203-1219 - 2023
Sebastián Elías Graiff Zurita, Kenji Kajiwara, Kenjiro T. Miura
We present an algorithm to fair a given planar curve by a log-aesthetic curve (LAC). We show how a general LAC segment can be uniquely characterized by seven parameters and present a method of parametric approximation based on this fact. This work aims to provide tools to be used in reverse engineering for computer-aided geometric design. Finally, we show an example of usage by applying this algor...... hiện toàn bộ
Matroid rank functions and discrete concavity
Springer Science and Business Media LLC - Tập 29 - Trang 535-546 - 2012
Akiyoshi Shioura
We discuss the relationship between matroid rank functions and a concept of discrete concavity called $${{\rm M}^{\natural}}$$ -concavity. It is known that a matroid rank function and its weighted version called a weighted rank function are ...... hiện toàn bộ
Symmetric finite element computation of convection-diffusion equations on a URR machine
Springer Science and Business Media LLC - Tập 8 - Trang 153-163 - 1991
Masahisa Tabata, Yoshiichi Ozeki, Hozumi Hamada
We approximate convection-diffusion equations with irrotational flows by a symmetric finite element formulation. Since very large real numbers appear in this formulation, we realize it on a URR (an internal representation method of real numbers) machine where practically no overflow/underflow occurs. Numerical results show that this formulation is applicable for sufficiently high Peclet number pro...... hiện toàn bộ
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