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A Fractional LC − RC Circuit

Ayoub, N., Alzoubi, F., Khateeb, H., Al-Qadi, M., Hasan (Qaseer), M., Albiss, B., Rousan, A. (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution which shows how the...

A free boundary problem for a predator-prey model with nonlinear prey-taxis

Mohsen Yousefnezhad, Seyyed Abbas Mohammadi, Farid Bozorgnia (2018)

Applications of Mathematics

This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary...

A free boundary problem for some modified predator-prey model in a higher dimensional environment

Hongmei Cheng, Qinhe Fang, Yang Xia (2022)

Applications of Mathematics

We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as t goes to infinity and survives in the new environment, or it fails to establish...

A free boundary stationary magnetohydrodynamic problem in connection with the electromagnetic casting process

Tomasz Roliński (1995)

Annales Polonici Mathematici

We investigate the behaviour of the meniscus of a drop of liquid aluminium in the neighbourhood of a state of equilibrium under the influence of weak electromagnetic forces. The mathematical model comprises both Maxwell and Navier-Stokes equations in 2D. The meniscus is governed by the Young-Laplace equation, the data being the jump of the normal stress. To show the existence and uniqueness of the solution we use the classical implicit function theorem. Moreover, the differentiability of the operator...

A free boundary value problem in potential theory

Guido Stampacchia, D. Kinderlehrer (1975)

Annales de l'institut Fourier

This paper is devoted to the formulation and solution of a free boundary problem for the Poisson equation in the plane. The object is to seek a domain Ω and a function u defined in Ω satisfying the given differential equation together with both Dirichlet and Neumann type data on the boundary of Ω . The Neumann data are given in a manner which permits reformulation of the problem as a variational inequality. Under suitable hypotheses about the given data, it is shown that there exists a unique solution...

A frictional contact problem with wear and damage for electro-viscoelastic materials

Mohamed Selmani, Lynda Selmani (2010)

Applications of Mathematics

We consider a quasistatic contact problem for an electro-viscoelastic body. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We present a weak formulation for the model and establish existence and uniqueness results. The proofs are based on classical results for elliptic variational...

A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme

Hyam Abboud, Toni Sayah (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We study a two-grid scheme fully discrete in time and space for solving the Navier-Stokes system. In the first step, the fully non-linear problem is discretized in space on a coarse grid with mesh-size H and time step k. In the second step, the problem is discretized in space on a fine grid with mesh-size h and the same time step, and linearized around the velocity uH computed in the first step. The two-grid strategy is motivated by the fact that under suitable assumptions, the contribution of uH...

A full multigrid method for semilinear elliptic equation

Fei Xu, Hehu Xie (2017)

Applications of Mathematics

A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as...

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