Mathematical Methods in the Applied Sciences

Items from 1 to 20 out of 7,131 results

article

Leray–Schauder alternatives for weakly sequentially continuous mappings and application to transport equation

Afif Ben Amar, Maher Mnif

Mathematical Methods in the Applied Sciences > 33 > 1 > 80 - 90

Motivated by the study of a general radiative transfer problem, we state some new variants of Leray–Schauder type fixed point theorems for weakly sequentially continuous operators. Further, we apply our results to establish some new existence and locality principles for a source problem in L₁‐setting with generally boundary conditions. Copyright © 2009 John Wiley & Sons, Ltd.

article

Boundary integral equations for bending of thermoelastic plates with transmission boundary conditions

I. Chudinovich, C. Constanda

Mathematical Methods in the Applied Sciences > 33 > 1 > 117 - 124

The solution of an initial‐boundary value problem for bending of a piecewise‐homogeneous thermoelastic plate with transverse shear deformation is represented as various combinations of single‐layer and double‐layer time‐dependent potentials. The unique solvability of the boundary integral equations generated by these representations is proved in spaces of distributions. Copyright © 2009 John Wiley...

article

A remark on free boundary problem of 1‐D compressible Navier–Stokes equations with density‐dependent viscosity

Changsheng Dou, Quansen Jiu

Mathematical Methods in the Applied Sciences > 33 > 1 > 103 - 116

In this paper, we prove the existence and uniqueness of the weak solution of the one‐dimensional compressible Navier–Stokes equations with density‐dependent viscosity µ(ρ)=ρ^θ with θ∈(0, γ⊲2], γ>1. The initial data are a perturbation of a corresponding steady solution and continuously contact with vacuum on the free boundary. The obtained results apply for the one‐dimensional Siant–Venant model...

article

On output functionals of boundary value problems on stochastic domains

Helmut Harbrecht

Mathematical Methods in the Applied Sciences > 33 > 1 > 91 - 102

We consider the computation of output functionals of random solutions to elliptic boundary value problems in domains with random boundary perturbations. We use a second‐order shape calculus to linearize the problem around a fixed nominal domain. For known mean and two‐point correlation function of the boundary perturbation, we derive, with leading order, deterministic expressions for the mean and...

article

Decay and nonexistence of global solutions of a quasilinear riser equation

Jorge A. Esquivel‐Avila

Mathematical Methods in the Applied Sciences > 33 > 1 > 71 - 79

We study qualitative properties of a quasilinear wave equation of fourth order that models the mechanical vibrations of a marine riser. Our analysis characterizes global and nonglobal solutions with respect to the norm of some Hilbert space, if energy is strictly less than the potential well depth. We employ invariant sets to show our results. In particular, we show that globality implies exponential...

article

The steady states and convergence to equilibria for a 1‐D chemotaxis model with volume‐filling effect

Yanyan Zhang

Mathematical Methods in the Applied Sciences > 33 > 1 > 25 - 40

We consider a chemotaxis model with volume‐filling effect introduced by Hillen and Painter. They also proved the existence of global solutions for a compact Riemannian manifold without boundary. Moreover, the existence of a global attractor in W^{1, p}(Ω⊂ℝⁿ), p>n, p⩾2, was proved by Wrzosek. He also proved that the ω‐limit set consists of regular stationary solutions. In this paper, we prove that...

article

Mixed nonlocal problem for a nonlinear singular hyperbolic equation

Said Mesloub

Mathematical Methods in the Applied Sciences > 33 > 1 > 57 - 70

In this paper, we study a nonlocal mixed problem for a nonlinear hyperbolic equation. Based on some a priori estimates and some density arguments, we prove the well posedness of the associated linear problem. The existence and uniqueness of the weak solution of the nonlinear problem are then established by applying an iterative process based on the obtained results for the linear problem. Copyright...

article

A monotone scheme for Hamilton–Jacobi equations via the nonstandard finite difference method

Roumen Anguelov, Jean M.‐S. Lubuma, Froduald Minani

Mathematical Methods in the Applied Sciences > 33 > 1 > 41 - 48

A usual way of approximating Hamilton–Jacobi equations is to couple space finite element discretization with time finite difference discretization. This classical approach leads to a severe restriction on the time step size for the scheme to be monotone. In this paper, we couple the finite element method with the nonstandard finite difference method, which is based on Mickens' rule of nonlocal approximation...

article

Does a ‘volume‐filling effect’ always prevent chemotactic collapse?

Michael Winkler

Mathematical Methods in the Applied Sciences > 33 > 1 > 12 - 24

The parabolic–parabolic Keller–Segel system for chemotaxis phenomena, is considered under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂ℝⁿ with n⩾2. It is proved that if ψ(u)/ϕ(u) grows faster than u^2/n as u→∞ and some further technical conditions are fulfilled, then there exist solutions that blow up in either finite or infinite time. Here, the total mass ∫_Ωu(x, t)dx may attain...

article

A non‐autonomous epidemic model with time delay and vaccination

Tailei Zhang, Junli Liu, Zhidong Teng

Mathematical Methods in the Applied Sciences > 33 > 1 > 1 - 11

In this paper, a non‐autonomous SIRVS epidemic model with time delay and vaccination is investigated. We assume that the vaccinated have a constant immunity period. Some new threshold conditions are obtained. These threshold conditions govern the extinction and permanence of the disease. When the model degenerates into the periodic or autonomous case, the corresponding basic reproduction number can...

article

Elliptic equations in weighted Sobolev spaces of infinite order with L¹ data

Mostafa Bendahmane, Moussa Chrif, Said El Manouni

Mathematical Methods in the Applied Sciences > 33 > 1 > 49 - 56

We deal with the existence and uniqueness of weak solutions for a class of strongly nonlinear boundary value problems of higher order with L¹ data in anisotropic‐weighted Sobolev spaces of infinite order. Copyright © 2009 John Wiley & Sons, Ltd.

article

A general theoretical model for the magnetohydrodynamic flow of micropolar magnetic fluids. Application to Stokes flow

P. M. Hatzikonstantinou, P. Vafeas

Mathematical Methods in the Applied Sciences > 33 > 2 > 233 - 248

Many practical applications, which have an inherent interest of physical and mathematical nature, involve the hydrodynamic flow in the presence of a magnetic field. Magnetic fluids comprise a novel class of engineering materials, where the coexistence of liquid and magnetic properties provides us with the opportunity to solve problems with high mathematical and technical complexity. Here, our purpose...

article

Relaxing convergence conditions for Stirling's method

S. K. Parhi, D. K. Gupta

Mathematical Methods in the Applied Sciences > 33 > 2 > 224 - 232

The aim of this paper is to study the convergence of Stirling's method used for finding fixed points of nonlinear operator equations assuming that the first Fréchet derivative of the nonlinear operator be ω‐conditioned. The ω‐condition relaxes the Lipschitz/Hölder condition on the first Fréchet derivative used earlier for the convergence. The existence and uniqueness regions are derived for the fixed...

article

Existence of positive solutions for nonlinear singular boundary value problem with p‐Laplacian

Dehong Ji, Yitao Yang, Weigao Ge

Mathematical Methods in the Applied Sciences > 33 > 2 > 188 - 197

In this paper, we study the existence of positive solutions for the following Sturm–Liouville‐like four‐point singular boundary value problem (BVP) with p‐Laplacian where ϕ_p(s)=|s|^p−2s, p>1, f is a lower semi‐continuous function. Using the fixed‐point theorem of cone expansion and compression of norm type, the existence of positive solution and infinitely many positive solutions for Sturm–Liouville‐like...

article

Analysis of a class of potential Korteweg‐de Vries‐like equations

R. M. Edelstein, K. S. Govinder

Mathematical Methods in the Applied Sciences > 33 > 2 > 138 - 146

We analyze a class of third‐order evolution equations, i.e. u_t = f(x, u_x, u_xx) u_xxx+g(x, u_x, u_xx) via the method of preliminary group classification. This method is a systematic means of analyzing the equation for symmetries. We find explicit forms of f and g, which allow for a larger dimensional Lie algebra of point symmetries. Copyright © 2009 John Wiley & Sons, Ltd.

article

Monotonicity methods in generalized Orlicz spaces for a class of non‐Newtonian fluids

Piotr Gwiazda, Agnieszka Świerczewska‐Gwiazda, Aneta Wróblewska

Mathematical Methods in the Applied Sciences > 33 > 2 > 125 - 137

The paper concerns existence of weak solutions to the equations describing a motion of some non‐Newtonian fluids with non‐standard growth conditions of the Cauchy stress tensor. Motivated by the fluids of strongly inhomogeneous behavior and having the property of rapid shear thickening, we observe that the L^p framework is not suitable to capture the described situation. We describe the growth conditions...

article

New exact solutions for seventh‐order Sawada–Kotera–Ito, Lax and Kaup–Kupershmidt equations using Exp‐function method

D. D. Ganji, A. G. Davodi, Y. A. Geraily

Mathematical Methods in the Applied Sciences > 33 > 2 > 167 - 176

In this work, Exp‐function method is used to solve three different seventh‐order nonlinear partial differential KdV equations. Sawada–Kotera–Ito, Lax and Kaup–Kupershmidt equations are well known and considered for solve. Exp‐function method can be used as an alternative to obtain analytic and approximate solutions of different types of differential equations applied in engineering mathematics. Ultimately...

article

Application of amplitude–frequency formulation to nonlinear oscillation system of the motion of a rigid rod rocking back

S. S. Ganji, D. D. Ganji, H. Babazadeh, N. Sadoughi

Mathematical Methods in the Applied Sciences > 33 > 2 > 157 - 166

The scope of this paper is evaluating an oscillation system with nonlinearities, using a periodic solution called amplitude–frequency formulation, such as the motion of a rigid rod rocking back. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. We are to compare the solutions results of this method with the exact...

article

Global attractors for 2‐D wave equations with displacement‐dependent damping

A. Kh. Khanmamedov

Mathematical Methods in the Applied Sciences > 33 > 2 > 177 - 187

In this paper the long‐time behaviour of the solutions of 2‐D wave equation with a damping coefficient depending on the displacement is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H

_{1}^{0}

(Ω) × L₂(Ω) and H²(Ω)∩H

_{1}^{0}

(Ω) × H

_{1}^{0}

article

Elliptic equations in highly heterogeneous porous media

Li‐Ming Yeh

Mathematical Methods in the Applied Sciences > 33 > 2 > 198 - 223

Uniform estimate and convergence for highly heterogeneous elliptic equations are concerned. The domain considered consists of a connected fractured subregion (with high permeability) and a disconnected matrix block subregion (with low permeability). Let ε denote the size ratio of one matrix block to the whole domain and let the permeability ratio of the matrix block region to the fractured region...

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Mathematical Methods in the Applied Sciences

Leray–Schauder alternatives for weakly sequentially continuous mappings and application to transport equation

Boundary integral equations for bending of thermoelastic plates with transmission boundary conditions

A remark on free boundary problem of 1‐D compressible Navier–Stokes equations with density‐dependent viscosity

On output functionals of boundary value problems on stochastic domains

Decay and nonexistence of global solutions of a quasilinear riser equation

The steady states and convergence to equilibria for a 1‐D chemotaxis model with volume‐filling effect

Mixed nonlocal problem for a nonlinear singular hyperbolic equation

A monotone scheme for Hamilton–Jacobi equations via the nonstandard finite difference method

Does a ‘volume‐filling effect’ always prevent chemotactic collapse?

A non‐autonomous epidemic model with time delay and vaccination

Elliptic equations in weighted Sobolev spaces of infinite order with L¹ data

A general theoretical model for the magnetohydrodynamic flow of micropolar magnetic fluids. Application to Stokes flow

Relaxing convergence conditions for Stirling's method

Existence of positive solutions for nonlinear singular boundary value problem with p‐Laplacian

Analysis of a class of potential Korteweg‐de Vries‐like equations

Monotonicity methods in generalized Orlicz spaces for a class of non‐Newtonian fluids

New exact solutions for seventh‐order Sawada–Kotera–Ito, Lax and Kaup–Kupershmidt equations using Exp‐function method

Application of amplitude–frequency formulation to nonlinear oscillation system of the motion of a rigid rod rocking back

Global attractors for 2‐D wave equations with displacement‐dependent damping

Elliptic equations in highly heterogeneous porous media

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