amin boumenir - Academia.edu (original) (raw)

Papers by amin boumenir

Research paper thumbnail of On the numerical inversion of the Laplace transform by the use of an optimized Legendre polynomials

Approximation Theory and its Applications

ABSTRACT

Research paper thumbnail of Series solutions for KPP type equations

Differential and Integral Equations

Research paper thumbnail of Title: Blow up of series solutions on the half line

We prove the convergence of series solutions of a semilinear reaction diffusion equation with a q... more We prove the convergence of series solutions of a semilinear reaction diffusion equation with a quadratic nonlinearity on the half line. We construct a positive solution that blows up in finite time. The algorithm employs algebraic operations only, which can be used to approximate and extend these solutions beyond blow up. All are welcome.

Research paper thumbnail of Sampling for multi-parameter spectral theory

Research paper thumbnail of Reconstructing the wave speed and the source

Mathematical Methods in the Applied Sciences, 2021

We are concerned with the inverse problem of recovering the unknown wave speed and also the sourc... more We are concerned with the inverse problem of recovering the unknown wave speed and also the source in a multidimensional wave equation. We show that the wave speed coefficient can be reconstructed from the observations of the solution taken at a single point. For the source, we may need a sequence of observation points due to the presence of multiple spectrum and nodal lines. This new method, based on spectral estimation techniques, leads to a simple procedure that delivers both uniqueness and reconstruction of the coefficients at the same time.

Research paper thumbnail of The impedance tomography problem

Proceedings of the American Mathematical Society, 2003

Using an operator theoretic framework and pseudo-spectral methods, we provide a simple and explic... more Using an operator theoretic framework and pseudo-spectral methods, we provide a simple and explicit formula for the conductivity coefficient in terms of the Dirichlet to Neumann map and the eigenvalues of the Laplacian operator.

Research paper thumbnail of Reconstructing The Moore-Gibson-Thompson Equation

Nonautonomous Dynamical Systems, 2020

We are concerned with the inverse problem of recovering a third order Moore-Gibson-Thompson equat... more We are concerned with the inverse problem of recovering a third order Moore-Gibson-Thompson equation from a single observation of its solution at an arbitrary point. We show how to reconstruct its three unknown parameters and the memory kernel by using the Laplace transform.

Research paper thumbnail of The reconstruction of an equation of visco-elasticity

Nonautonomous Dynamical Systems, 2018

We are concerned with the reconstruction of two coefficients of an integro-differential equation ... more We are concerned with the reconstruction of two coefficients of an integro-differential equation modeling the deformation of materials with memory.We show that we can explicitly reconstruct the memory, the source terms and the diffusion constant from two observations only.

Research paper thumbnail of A solvability condition for a Tokamak problem

Journal of Spectral Theory, 2017

Research paper thumbnail of Higher Approximation of Eigenvalues by the Sampling Method

Bit Numerical Mathematics, Jun 1, 2000

Research paper thumbnail of Level sets for reaction diffusion equations

We are concerned with the shape of the level sets of solution of reaction diffusion equations. Us... more We are concerned with the shape of the level sets of solution of reaction diffusion equations. Using the maximum principle we find sufficient conditions for their concavity.

Research paper thumbnail of Identification of a wave equation generated by a string

ESAIM: Control, Optimisation and Calculus of Variations, 2014

Research paper thumbnail of Reconstruction of the Refraction Index in Stratified Ocean

SIAM Journal on Applied Mathematics, 2011

ABSTRACT The paper deals with an inverse problem arising in harmonic acoustics in ocean, where th... more ABSTRACT The paper deals with an inverse problem arising in harmonic acoustics in ocean, where the concern is the reconstruction of the acoustic refraction index. A set of uniqueness for the reconstruction of the index is provided. It is also shown that one measurement of acoustic waves at the surface and bottom is enough to reconstruct the acoustic refraction index if it is known close to the surface.

Research paper thumbnail of Frequency modules and nonexistence of quasi-periodic solutions of nonlinear evolution equations

Semigroup Forum, 2007

... Amin Boumenir · Nguyen Van Minh · Vu Kim Tuan ... A. Boumenir · NV Minh ( ) · VK Tuan Departm... more ... Amin Boumenir · Nguyen Van Minh · Vu Kim Tuan ... A. Boumenir · NV Minh ( ) · VK Tuan Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA e-mail: vnguyen@westga. edu A. Boumenir e-mail: boumenir@westga.edu VK Tuan e-mail: vu@westga ...

Research paper thumbnail of Computing eigenvalues of Sturm-Liouville systems of Bessel type

Proceedings of the Edinburgh Mathematical Society, 1999

In this paper we shall develop a new method for the computation of eigenvalues of singular Sturm-... more In this paper we shall develop a new method for the computation of eigenvalues of singular Sturm-Liouville problems of the Bessel type. This new method is based on the interpolation of a boundary function in Paley-Wiener spaces. Numerical results are provided to illustrate the method.

Research paper thumbnail of Direct computation of the spectral function

Proceedings of the American Mathematical Society, 1995

We would like to find an explicit formula for the spectral function of the following Sturm-Liouvi... more We would like to find an explicit formula for the spectral function of the following Sturm-Liouville problem: \[ { L f ≡ − d 2 d x 2 f ( x ) + q ( x ) f ( x ) , x ≥ 0 , f ′ ( 0 ) − m f ( 0 ) = 0. \left \{ {\begin {array}{*{20}{c}} {Lf \equiv - \frac {{{d^2}}}{{d{x^2}}}f(x) + q(x)f(x),\quad x \geq 0,} \hfill \\ {f’(0) - mf(0) = 0.} \hfill \\ \end {array} } \right . \] A simple operational calculus argument will help us obtain an explicit formula for the transmutation kernel. The expression of the spectral function is then obtained through the nonlinear integral equation found in the Gelfand-Levitan theory.

Research paper thumbnail of A finite inverse problem by the determinant method

Operators and Matrices, 2009

Research paper thumbnail of Toward a general theory of transmutation

Nonlinear Analysis: Theory, Methods & Applications, 1996

Research paper thumbnail of The approximation of the transmutation kernel

Journal of Mathematical Physics, 2006

The transformation operator plays an important role in the direct and inverse spectral theory of ... more The transformation operator plays an important role in the direct and inverse spectral theory of Sturm-Liouville operators. In this paper we would like to approximate the kernel of the transformation operator used in the Gelfand-Levitan theory. The analytic properties of the solution allows for its representation by either a Taylor series about the diagonal or a Fourier cosine series. Example illustrating how the coefficients can be computed are provided.

Research paper thumbnail of Inverse Spectral Problem for the Laguerre Differential Operator

Journal of Mathematical Analysis and Applications, 1998

Research paper thumbnail of On the numerical inversion of the Laplace transform by the use of an optimized Legendre polynomials

Approximation Theory and its Applications

ABSTRACT

Research paper thumbnail of Series solutions for KPP type equations

Differential and Integral Equations

Research paper thumbnail of Title: Blow up of series solutions on the half line

We prove the convergence of series solutions of a semilinear reaction diffusion equation with a q... more We prove the convergence of series solutions of a semilinear reaction diffusion equation with a quadratic nonlinearity on the half line. We construct a positive solution that blows up in finite time. The algorithm employs algebraic operations only, which can be used to approximate and extend these solutions beyond blow up. All are welcome.

Research paper thumbnail of Sampling for multi-parameter spectral theory

Research paper thumbnail of Reconstructing the wave speed and the source

Mathematical Methods in the Applied Sciences, 2021

We are concerned with the inverse problem of recovering the unknown wave speed and also the sourc... more We are concerned with the inverse problem of recovering the unknown wave speed and also the source in a multidimensional wave equation. We show that the wave speed coefficient can be reconstructed from the observations of the solution taken at a single point. For the source, we may need a sequence of observation points due to the presence of multiple spectrum and nodal lines. This new method, based on spectral estimation techniques, leads to a simple procedure that delivers both uniqueness and reconstruction of the coefficients at the same time.

Research paper thumbnail of The impedance tomography problem

Proceedings of the American Mathematical Society, 2003

Using an operator theoretic framework and pseudo-spectral methods, we provide a simple and explic... more Using an operator theoretic framework and pseudo-spectral methods, we provide a simple and explicit formula for the conductivity coefficient in terms of the Dirichlet to Neumann map and the eigenvalues of the Laplacian operator.

Research paper thumbnail of Reconstructing The Moore-Gibson-Thompson Equation

Nonautonomous Dynamical Systems, 2020

We are concerned with the inverse problem of recovering a third order Moore-Gibson-Thompson equat... more We are concerned with the inverse problem of recovering a third order Moore-Gibson-Thompson equation from a single observation of its solution at an arbitrary point. We show how to reconstruct its three unknown parameters and the memory kernel by using the Laplace transform.

Research paper thumbnail of The reconstruction of an equation of visco-elasticity

Nonautonomous Dynamical Systems, 2018

We are concerned with the reconstruction of two coefficients of an integro-differential equation ... more We are concerned with the reconstruction of two coefficients of an integro-differential equation modeling the deformation of materials with memory.We show that we can explicitly reconstruct the memory, the source terms and the diffusion constant from two observations only.

Research paper thumbnail of A solvability condition for a Tokamak problem

Journal of Spectral Theory, 2017

Research paper thumbnail of Higher Approximation of Eigenvalues by the Sampling Method

Bit Numerical Mathematics, Jun 1, 2000

Research paper thumbnail of Level sets for reaction diffusion equations

We are concerned with the shape of the level sets of solution of reaction diffusion equations. Us... more We are concerned with the shape of the level sets of solution of reaction diffusion equations. Using the maximum principle we find sufficient conditions for their concavity.

Research paper thumbnail of Identification of a wave equation generated by a string

ESAIM: Control, Optimisation and Calculus of Variations, 2014

Research paper thumbnail of Reconstruction of the Refraction Index in Stratified Ocean

SIAM Journal on Applied Mathematics, 2011

ABSTRACT The paper deals with an inverse problem arising in harmonic acoustics in ocean, where th... more ABSTRACT The paper deals with an inverse problem arising in harmonic acoustics in ocean, where the concern is the reconstruction of the acoustic refraction index. A set of uniqueness for the reconstruction of the index is provided. It is also shown that one measurement of acoustic waves at the surface and bottom is enough to reconstruct the acoustic refraction index if it is known close to the surface.

Research paper thumbnail of Frequency modules and nonexistence of quasi-periodic solutions of nonlinear evolution equations

Semigroup Forum, 2007

... Amin Boumenir · Nguyen Van Minh · Vu Kim Tuan ... A. Boumenir · NV Minh ( ) · VK Tuan Departm... more ... Amin Boumenir · Nguyen Van Minh · Vu Kim Tuan ... A. Boumenir · NV Minh ( ) · VK Tuan Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA e-mail: vnguyen@westga. edu A. Boumenir e-mail: boumenir@westga.edu VK Tuan e-mail: vu@westga ...

Research paper thumbnail of Computing eigenvalues of Sturm-Liouville systems of Bessel type

Proceedings of the Edinburgh Mathematical Society, 1999

In this paper we shall develop a new method for the computation of eigenvalues of singular Sturm-... more In this paper we shall develop a new method for the computation of eigenvalues of singular Sturm-Liouville problems of the Bessel type. This new method is based on the interpolation of a boundary function in Paley-Wiener spaces. Numerical results are provided to illustrate the method.

Research paper thumbnail of Direct computation of the spectral function

Proceedings of the American Mathematical Society, 1995

We would like to find an explicit formula for the spectral function of the following Sturm-Liouvi... more We would like to find an explicit formula for the spectral function of the following Sturm-Liouville problem: \[ { L f ≡ − d 2 d x 2 f ( x ) + q ( x ) f ( x ) , x ≥ 0 , f ′ ( 0 ) − m f ( 0 ) = 0. \left \{ {\begin {array}{*{20}{c}} {Lf \equiv - \frac {{{d^2}}}{{d{x^2}}}f(x) + q(x)f(x),\quad x \geq 0,} \hfill \\ {f’(0) - mf(0) = 0.} \hfill \\ \end {array} } \right . \] A simple operational calculus argument will help us obtain an explicit formula for the transmutation kernel. The expression of the spectral function is then obtained through the nonlinear integral equation found in the Gelfand-Levitan theory.

Research paper thumbnail of A finite inverse problem by the determinant method

Operators and Matrices, 2009

Research paper thumbnail of Toward a general theory of transmutation

Nonlinear Analysis: Theory, Methods & Applications, 1996

Research paper thumbnail of The approximation of the transmutation kernel

Journal of Mathematical Physics, 2006

The transformation operator plays an important role in the direct and inverse spectral theory of ... more The transformation operator plays an important role in the direct and inverse spectral theory of Sturm-Liouville operators. In this paper we would like to approximate the kernel of the transformation operator used in the Gelfand-Levitan theory. The analytic properties of the solution allows for its representation by either a Taylor series about the diagonal or a Fourier cosine series. Example illustrating how the coefficients can be computed are provided.

Research paper thumbnail of Inverse Spectral Problem for the Laguerre Differential Operator

Journal of Mathematical Analysis and Applications, 1998