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Items from 1 to 20 out of 201 results

article

Stable recovery of noncompactly supported electromagnetic potentials in unbounded domain

Yavar Kian, Yosra Soussi

Mathematical Methods in the Applied Sciences > 44 > 17 > 13421 - 13447

We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of a general class of magnetic field and electric potential from boundary measurements. Assuming the knowledge of the unknown coefficients close to the boundary, we obtain other results of stable recovery with...

article

Uniform attractors of nonclassical diffusion equations on $ℝ^{N}$ with memory and singularly oscillating external forces

Thi Thuy Le, Duong Toan Nguyen

Mathematical Methods in the Applied Sciences > 44 > 1 > 820 - 852

In this paper, we consider a class of nonclassical diffusion equations on

ℝ^{N}

with hereditary memory, in presence of singularly oscillating external forces depending on a positive parameter ε and a new class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. Under a general assumption on the memory kernel κ and for a very large class of nonlinearities, we prove the...

article

A coupled system of fractional differential equations on the half-line

Chengbo Zhai, Jing Ren

Boundary Value Problems > 2019 > 2019 > 1 > 1-22

In this paper, we consider a new fractional differential system on an unbounded domain Dαu(t)+φ(t,v(t),Dγ1v(t))=0,t∈[0,+∞),α∈(2,3],Dβv(t)+ψ(t,u(t),Dγ2u(t))=0,t∈[0,+∞),β∈(2,3], $$\begin{aligned} &D^{\alpha }u(t)+\varphi \bigl(t,v(t),D^{\gamma _{1}}v(t)\bigr)=0, \quad t \in [0,+ \infty ), \alpha \in (2,3], \\ &D^{\beta }v(t)+\psi \bigl(t,u(t),D^{\gamma _{2}}u(t)\bigr)=0, \quad t\in [0,+\infty...

article

Anisotropic Degenerate Parabolic Problems in $$\mathbb {R}^N$$ RN with Variable Exponent and Locally Integrable Data

Fares Mokhtari, Rabah Mecheter

Mediterranean Journal of Mathematics > 2019 > 16 > 3 > 1-21

In this paper, we prove the existence and regularity of weak solutions for a class of nonlinear anisotropic parabolic equations in the whole $$(0,T)\times \mathbb {R}^N$$ (0,T)×RN with $$p_i(x)$$ pi(x) growth conditions and locally integrable data. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Our results are generalizations of the corresponding results in the...

article

An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions

Juan Casado-Díaz, Faustino Maestre

Revista Matemática Complutense > 2019 > 32 > 3 > 681-730

The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity...

article

The entropy solution of a reaction–diffusion equation on an unbounded domain

Huashui Zhan, Yongping Li

Journal of Inequalities and Applications > 2019 > 2019 > 1 > 1-23

The degenerate parabolic equations from the reaction–diffusion problems are considered on an unbounded domain Ω⊂RN $\varOmega\subset\mathbb {R}^{N}$. It is expected that only a partial boundary should be imposed the homogeneous boundary value, but how to give the analytic expression of this partial boundary seems very difficult. A new method, which is called the general characteristic function method,...

article

The Laguerre-Hermite spectral methods for the time-fractional sub-diffusion equations on unbounded domains

Hao Yu, Boying Wu, Dazhi Zhang

Numerical Algorithms > 2019 > 82 > 4 > 1221-1250

This study uses Laguerre-Hermite spectral Galerkin and spectral collocation methods for solving time-fractional sub-diffusion equations on unbounded domains. In the time domain, the generalized associated Laguerre functions of the first kind are employed as basis functions. In the Galerkin method, the fractional derivative of the basis functions can be obtained using the Laplace transform and its...

article

A numerical approach based on B-spline basis functions to solve boundary layer flow model of a non-Newtonian fluid

Kourosh Parand, Nastaran Bajalan

Journal of the Brazilian Society of Mechanical Sciences and Engineering > 2018 > 40 > 10 > 1-9

A spectral method based on B-spline functions is proposed for the numerical solution of the boundary layer flow of an Powell–Eyring fluid over a stretching sheet. First, the B-spline functions formula is represented, and the quasilinearization method is used to approximate the nonlinear equation of the problem with a sequence of linear equations. Then, the collocation method is used to approximate...

article

A singular Monge-Ampère equation on unbounded domains

Huaiyu Jian, You Li

Science China Mathematics > 2018 > 61 > 8 > 1473-1480

In this paper, we study the Dirichlet problem for a singular Monge-Ampère type equation on unbounded domains. For a few special kinds of unbounded convex domains, we find the explicit formulas of the solutions to the problem. For general unbounded convex domain Ω, we prove the existence for solutions to the problem in the space C^∞(Ω) ∩ C(Ω̅). We also obtain the local C^1/2-estimate up to the ∂Ω and...

article

An explicit spectral collocation method for the linearized Korteweg–de Vries equation on unbounded domain

Jinwei Fang, Boying Wu, Wenjie Liu

Applied Numerical Mathematics > 2018 > 126 > C > 34-52

In this paper, we present a stable and efficient numerical scheme for the linearized Korteweg–de Vries equation on unbounded domain. After employing the Crank–Nicolson method for temporal discretization, the transparent boundary conditions are derived for the time semi-discrete scheme. Then the unconditional stability of the resulting initial boundary problem is established. For spatial discretization,...

article

A Vortex Particle-Mesh method for subsonic compressible flows

Philippe Parmentier, Grégoire Winckelmans, Philippe Chatelain

Journal of Computational Physics > 2018 > 354 > C > 692-716

This paper presents the implementation and validation of a remeshed Vortex Particle-Mesh (VPM) method capable of simulating complex compressible and viscous flows. It is supplemented with a radiation boundary condition in order for the method to accommodate the radiating quantities of the flow. The efficiency of the methodology relies on the use of an underlying grid; it allows the use of a FFT-based...

article

Existence of ground state solutions for Kirchhoff‐type problems involving critical Sobolev exponents

Haining Fan

Mathematical Methods in the Applied Sciences > 41 > 1 > 371 - 385

In this paper, we study the existence of ground state solutions for a Kirchhoff‐type problem in

R^{3}

involving critical Sobolev exponent. With the help of Nehari manifold and the concentration‐compactness principle, we prove that problem admits at least one ground state solution.

article

Hybrid Chebyshev function bases for sparse spectral methods in parity-mixed PDEs on an infinite domain

Benjamin Miquel, Keith Julien

Journal of Computational Physics > 2017 > 349 > C > 474-500

We present a numerical spectral method to solve systems of differential equations on an infinite interval y∈(−∞,∞) in presence of linear differential operators of the form Q(y)(∂/∂y)b (where Q(y) is a rational fraction and b a positive integer). Even when these operators are not parity-preserving, we demonstrate how a mixed expansion in interleaved Chebyshev rational functions TBn(y) and SBn(y) preserves...

article

Numerical study of the influence of electrode arrangements in electrokinetic remediation technique

Gustavo Benitez Alvarez, Natanael Júnior Soares Bento, Tiago Araújo Neves, Fabiana Soares Dos Santos, more

Environmental Science and Pollution Research > 2017 > 24 > 34 > 26424- 26435

The effectiveness of electrokinetic remediation for soils depends on several factors such as the arrangement and shape of electrodes. This paper presents a numerical study on external electrostatic field generated by seven different electrode configurations in any unbounded two-dimensional domain. The boundary condition at infinity for the voltage is approximated by the iterative algorithm that expands...

article

Box-counting dimensions and upper semicontinuities of bi-spatial attractors for stochastic degenerate parabolic equations on an unbounded domain

Jinyan Yin, Yangrong Li, Hongyong Cui

Journal of Mathematical Analysis and Applications > 2017 > 450 > 2 > 1180-1207

The paper contributes box-counting dimensions and upper semicontinuities of random bi-spatial attractors for stochastic degenerate parabolic equations on the whole Euclid space. Under some weak assumptions for the force and the nonlinearity, we first prove the existence of a unique (L2,D01,2∩Lq)-random attractor for any q∈[2,(p−2)I+2], where p−1 is the order of the nonlinearity and I is a given integer...

chapter

A finite element based eigen-analysis of THz nanoantennas

Konstantinos D. Paschaloudis, Constantinos L. Zekios, Peter C. Allilomes, George A. Kyriacou

2017 IEEE MTT-S International Microwave Symposium (IMS) > 1902 - 1905

2017 IEEE/MTT-S International Microwave Symposium - IMS 2017

The establishment of a rigorous full-wave eigenanalysis based on finite element method as numerical tool for the understanding and the revealing the characteristics of Terahertz nano-antennas, constitutes the scope of the current work. A tree-cotree splitting formulation method is incorporated for the suppression of all types of spurious modes. An indicative example of a gold nanodimer structure is...

article

A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains

Er‐xiang Song, Shuang Luo

International Journal for Numerical and Analytical Methods in Geomechanics > 41 > 8 > 1108 - 1124

Numerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical...

article

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

Sebastian Liska, Tim Colonius

Journal of Computational Physics > 2017 > 331 > C > 257-279

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method,...

article

Perfectly matched layers for convex truncated domains with discontinuous Galerkin time domain simulations

Axel Modave, Jonathan Lambrechts, Christophe Geuzaine

Computers & Mathematics with Applications > 2017 > 73 > 4 > 684-700

This paper deals with the design of perfectly matched layers (PMLs) for transient acoustic wave propagation in generally-shaped convex truncated domains. After reviewing key elements to derive PML equations for such domains, we present two time-dependent formulations for the pressure–velocity system. These formulations are obtained by using a complex coordinate stretching of the time-harmonic version...

article

On the existence and uniqueness of time periodic solutions for a semilinear heat equation in the whole space

Jian Deng

Mathematical Methods in the Applied Sciences > 40 > 3 > 796 - 802

This paper is concerned with the existence and uniqueness of time periodic solutions in the whole‐space

R^{N}

for a heat equation with nonlinear term. The nonlinear term we considered is of this type, |u|^{q − 1}u + f(x,t), with

q > \frac{N}{N - 2}

, N > 2. We show that there exists a unique time periodic solution when the source term f is small. In fact,

\frac{N}{N - 2}

is a critical exponent; when

1 < q \leq \frac{N}{N - 2}

, there...

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Search results

Stable recovery of noncompactly supported electromagnetic potentials in unbounded domain

Uniform attractors of nonclassical diffusion equations on $ℝ^{N}$ with memory and singularly oscillating external forces

A coupled system of fractional differential equations on the half-line

Anisotropic Degenerate Parabolic Problems in $$\mathbb {R}^N$$ RN with Variable Exponent and Locally Integrable Data

An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions

The entropy solution of a reaction–diffusion equation on an unbounded domain

The Laguerre-Hermite spectral methods for the time-fractional sub-diffusion equations on unbounded domains

A numerical approach based on B-spline basis functions to solve boundary layer flow model of a non-Newtonian fluid

A singular Monge-Ampère equation on unbounded domains

An explicit spectral collocation method for the linearized Korteweg–de Vries equation on unbounded domain

A Vortex Particle-Mesh method for subsonic compressible flows

Existence of ground state solutions for Kirchhoff‐type problems involving critical Sobolev exponents

Hybrid Chebyshev function bases for sparse spectral methods in parity-mixed PDEs on an infinite domain

Numerical study of the influence of electrode arrangements in electrokinetic remediation technique

Box-counting dimensions and upper semicontinuities of bi-spatial attractors for stochastic degenerate parabolic equations on an unbounded domain

A finite element based eigen-analysis of THz nanoantennas

A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

Perfectly matched layers for convex truncated domains with discontinuous Galerkin time domain simulations

On the existence and uniqueness of time periodic solutions for a semilinear heat equation in the whole space

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