قسم الرياضيات
On one-dimensional fox-rabies dynamics of advection type
Saleem A. Obaidat* and M.R. Abo Elrish
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455,
Riyadh 11451, Saudi Arabia
(Received 16 June 2009; revised version received 24 June 2010; second revision received 25 October 2010;
accepted 18 November 2010 )
A one-dimensional model of fox-rabies of two nonlinear partial differential equations of hyperbolic type is studied. Finite difference techniques are applied to compute the numerical solutions of the initial/boundary value problem. The convergence of the resulting schemes, which have a second order accuracy in space and time, is investigated. The method is tested for different values of advection rate; numerical and graphical results showed that the method is consistent with the dynamic behaviour of fox-rabies.
Keywords: hyperbolic type; initial/boundary value problem; finite-difference method; fox-rabies; advection model; truncation errors.
SINGULAR LIMITS SOLUTION FOR $2$-DIMENSIONAL ELLIPTIC PROBLEMS INVOLVING
EXPONENTIAL NONLINEARITIES WITH NONLINEAR
GRADIENT TERMS AND SINGULAR WEIGHTS
Sami BARAKET Imed ABID and Taieb OUNI
Annali di Matematica
Abstract: Given $\Omega$ bounded open regular set of $\R^2$, $q_1, \cdots, q_K \in \Omega$, $\varrho : \Omega \longrightarrow [0,+\infty)$ a regular bounded function and $V: \Omega \longrightarrow [0,+\infty)$ a bounded function. We give a sufficient condition for the model problem\[(P): -\Delta u -\lambda \varrho(x)|\nabla u|^2= \e^{2}V(x) e^u\] to have a positive weak solution in $\Omega$ with $ u = 0$ on $\partial \Omega$, which is singular at each $q_i$ as the parameters $\e$ and $\lambda$ tend to $0$, essentially when the set of concentration points $q_i$ and the set of zeros of $V$ are not necessarily disjoint.
Powers of the fixed points of the Gauss map
Tariq A. Al-Fadhel
alfadhel@ksu.edu.sa
Abstract
This paper shows that any odd power of any fixed point of the Gauss map is also a fixed point of th Gauss map, and gives its specific continued fraction form. This paper also shows that any even power of any fixed point of the Gauss map is an inverse image of a specific 2-cycle.
Key words: 1. The Gauss map 2. Continued fraction 3.fixed point 2000 Math subject classification 30B70 , 11A55 .
Solitary wave solutions of the improved KdV equation by VIM
Saleh M. Hassan and Naif. M. Alotaibi
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, KSA
smhm@ksu.edu.sa; salehmh@hotmail.com
Abstract
The variational iteration method (VIM) is applied to solve numerically the improved Korteweg-de Vries equation (IKdV). A correction function is constructed with a general Lagrange multiplier that can be identified optimally via the variational theory. This technique provides a sequence of functions with easily computable components that converge rapidly to the exact solution of the IKdV equation. Propagation of single, interaction of two, and three solitary waves, and also birth of solitons have been discussed. Three invariants of motion have been evaluated to determine the conservation properties of the problem. This procedure is promising for solving other nonlinear equations.
Key words: Improved KdV equation; solitary waves; variational iteration method.
Numerical computation of BCOPs in two variables for solving the vibration problem of a CF-elliptical plate
Saleh M. Hassan
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, KSA
Abstract
Boundary characteristic orthogonal polynomials in xy-coordinates have been built up over an elliptical domain occupied by a thin elastic plate. Half of the plate boundary is taken clamped while the other half is kept free. Coefficients of these polynomials have been computed once and for all so that an orthogonal polynomial sequence is generated from a set of linearly independent functions satisfying the essential boundary conditions of the problem. Use of this sequence in Rayleigh-Ritz method for solving the free vibration problem of the plate makes it faster in convergence and leads to a simplified system whose solution is comparatively easier. Three dimensional solution surfaces and the associated contour lines have been plotted in some selected cases. Comparison have been made with known results whenever available.
Key words: Elliptical plates; nonuniform boundary conditions; orthogonal polynomials; vibration.
Advanced Nonlinear Studies 10 (2010), 771{788
The Wente Problem Associated to the Modi¯ed
Helmholtz Operator on Weighted Sobolev Spaces
Ines Ben Omrane
D¶epartement de Math¶ematiques
Facult¶e des Sciences de Tunis, Campus Universitaire, 2092 Tunis, Tunisia
e-mail: benomraneines@gmail.com
Mohamed Jleli¤
Department of Mathematics
King Saud University, Saudi Arabia
e-mail: jleli@ksu.edu.sa
Bessem Samet
D¶epartement de Math¶ematiques
Ecole Sup¶erieure des Sciences et Techniques de Tunis, 5 Avenue Taha Hussein, 1008, Tunisia
e-mail: bessem.samet@gmail.com
Communicated by Abbas Bahri
Abstract
In this paper, we give a weighted version of regularity of solutions of the Wente problem associated to the modi¯ed Helmholtz operator ¡¢ + ®I, where ® is a positive constant.
Nonlinear Differ. Equ. Appl.
_c 2010 Springer Basel AG
DOI 10.1007/s00030-010-0084-z
Nonlinear Differential Equations
and Applications NoDEA
Singular limits for 2-dimensional elliptic problem involving exponential nonlinearity with nonlinear gradient term
Sami Baraket, Ines Ben Omrane and Taieb Ouni
Abstract.
Given a bounded open regular set Ω ⊂R2 and x1, x2, . . . , xm ∈ Ω, we give a sufficient condition for the problem
−div(a(u)∇u) = ρ2f(u) to have a positive weak solution u in Ω with u = 0 on ∂Ω, which is singular at each xi as the parameter ρ tends to 0 and under suitable assumptions on exponential functions a(u) and f(u).
Mathematics Subject Classification (2000). 35J60, 53C21, 58J05.
Keywords. Singular limits, Green’s function, Nonlinear domain
decomposition method.
Applied Mathematical Sciences, Vol. 3, 2009, no. 11, 533 - 540
Exact Solutions for Some Reaction Diffusion
Systems with Nonlinear Reaction Polynomial Terms
E. S. Fahmy H. and A. Abdusalam
King Saud University, College of Science, Mathematics Department
Kingdom of Saudi Arabia hosny@ksu.edu.sa
Abstract
We introduce a method to find exact traveling wave solutions for reaction diffusion systems of equations with nonlinear reaction polynomial terms. We will apply the method on an important kinds of reaction diffusion systems, such as the model for the spatial spread of an epidemic, predator-prey two component telegraph model.
COMPACT SUBMANIFOLDS OF A EUCLIDEAN SPACE
Sharief Deshmukh
Department of Mathematics, College of Science, King Saud University, P.O. Box-2455, Riyadh-11451, Saudi Arabia
Abstract
In this paper we study compact submanifolds of the complex Euclidean space . Such a submanifold M of the Euclidean space has naturally defined linear operators φ, F, C and G (see section-3 for the definition). First we study the basic properties of these operators for a submanifold and then we prove non-immersibility results for compact Riemannian manifolds in the Euclidean space .We also obtain conditions under which a submanifold of the Euclidean space is a totally real submanifold or a CR-submanifold.
JP Journal of Geometry and Topology Volume …, Number …, Pages…
SPECTRUM OF AN EINSTEIN-LIKE MANIFOLD
SHARIEF DESHMUKH
Department of Mathematics
King Saud University
P. O. Box 2455, Riyadh 11451, Saudi Arabia
e-mail: shariefd@ksu.edu.sa
Abstract
In this paper, we obtain a lower bound for the nonzero eigenvalues of
Laplacian operator on a compact Einstein-like manifold (Riemannian
manifold with parallel Ricci tensor) similar to Simon’s result [9].
Hindawi Publishing Corporation
Journal of Inequalities and Applications
Volume 2009, Article ID 167403, 12 pages
doi:10.1155/2009/167403
On Some Quasimetrics and Their Applications
Imed Bachar and Habib Mâagli
Abstract: In this paper, we aim at giving a rich class of quasi-metrics from which we obtain as an application an interesting inequality for the Green function of the fractional Laplacian in a smooth domain in Rⁿ.
SOME PROPERTIES CONCERNING THE INDICIAL ROOTS OF THE
JACOBI OPERATOR ABOUT THE DELAUNAY HYPERSURFACE
MOHAMED JLELI
Department of Mathematics, College of Science, King Saud University.
P.O. Box 2455, Riyadh 11451, Saudia Arabia.
E-mail: jleli@ksu.edu.sa
Abstract.
In this paper, we prove a maximum principle of the Jacobi
operator of the Delaunay hypersurfaces and we study the positivity of
the indicial roots about these operators. We partially generalize, in any
dimension, the result of R. Kusner, R. Mazzeo and D. Pollack.
1991 Mathematics Subject Classification. 35J05, 53A07.
Key words. Mean curvature, Hypersurface
Dr. Assal miloud
College of Sciences
Department of Mathematics
Generalized Besov Type Spaces on The Dual of The Laguerre
Hypergroup
Abstract
In this paper we introduce the homogeneous Besov type spaces on the dual of
Laguerre hypergroup and we establish some new harmonic analysis results. We give some characterizations
of these spaces using equivalent seminorms. Also we study the non-homogeneous Besov type
spaces .We give some properties of these spaces and embeddings results with respect to their
parameters .
Keywords Laguerre hypergroup, Besov type spaces, Calder´on-reproducing formula.
MR(2000) Subject Classification 42B35, 35L35S
Gauss Map vs Bernoulli Shift
Tariq A. Al-Fadhel
alfadhel@ksu.edu.sa
Abstract
This paper shows that blocks of different entries and different lengths can have the same probability of occurence in the representation of any continued fraction which its orbit distributed according to Gauss measure. More precisely there are blocks of even lengths and 3-blocks which their probability of occurence equals to the probability of occurence of a unit block, and this property is not satisfied by the Bernoulli shift.
Keywords : Continued fractions, Gauss map, Bernoulli shift, Fibonacci sequence.
