Born at July 20, 1964 at Tripoli Lebanon.
 

ADDRESS:
P.O. box 155-012 Beirut Lebanon.
Tel. (961) (03) 658 632
Fax (961) (1) 865 087
Email :mjazar@ul.edu.lb
 
 

HIGHEST DEGREE: Ph. D., June 1991, Université de Poitiers France
 

TEACHING EXPERIENCE :
- 87-89:  Instructor at Université de Poitiers.
- 89-91:  Assistant at Université de Poitiers.
- 91-93:  Assistant Professor at Université de Poitiers.
- 93-98:  Associate Professor, Lebanese University, Math. Department
- 99--:  Professor, Lebanese University, Math. Department

INVITATIONS

Invitations to mathematics department for a period of two to four weeks:

•  Mars 95:                 University Poitiers France.
•  June 98:                   University Paris 13.
•  Sept 98:                   University Tunis 2.
•  June 99:                   University Paris 13.
•  July 99:                    University Poitiers.
•  Sept. 00:                 University Cadi Ayyad Morocco.
•  Oct .00:                   Univ. Ibn Zohr Morocco.
•  May 01:                  Univ. de Versailles.
•  June 01:                  Ulm university. Germany.
•  July 01:                    Univ. Paris 7.
• Feb-May 02:            University of Tours. France
• June 02:                    University Cadi Ayyad Morocco.

TEACHING DOMAINS

• Mathematics and computer courses for the first and second years.
• Analysis courses for third and fourth years: Topology, Integration, Fourier analysis, ODE, PDE and numerical analysis, Spectral theory, Distributions and Functional analysis.

RESEARCH ACTIVITY

• Spectral theory, regularized and integrated semigroups, and evolution equations.
• Perturbation results for spectral distributions.
• The wave equation inside and outside of a domain, numerical and theoretical study.
• Finite time blow-up, global existence and asymptotic behavior for semi-linear parabolic and wave equations.

Supervision of Master’s thesis

1. Steve YOUNAN. Résolution numérique de l’équation des ondes en domaine extérieur. DEA modélisation et calcul intensif. Novembre 1999.
2. Samuel NEHME. Explosion en temps fini d’une ODE non linéaire. DEA modélisation et calcul intensif. Janvier 2001.
3. Nissrine KASSEM. Comportement asymptotique des solutions de l’équation des ondes semi-linéaires. In preparation.
 

Supervision of Ph. D. thesis

1. Souad SAADE. Gevrey’s regularity of linear and semi linear Cauchy’s problems. In preparation.

PUBLICATIONS
 

1. Applications of Spectral Distributions to some Cauchy Problems in L^p(R^n), Trends in Semigroup Theory and Evolution Equations, Editions P. Clément...Marcel Dekker 1991 pages 143--151. (With H. Emamirad)

3. Fractional powers of the momentum of a spectral distribution, Proceedings of the American Mathematical Society, June 1995 volume 123 (6) pages 1805-1813.

4. Commuting multiplicative perturbations, Houston Journal of Mathematics volume 20 (3) 1994. (With R. deLaubenfels)

5. Regularized Spectral Distribution, Acta Applicandae Mathematicae volume 43 1996 pages 267-287. (With R. deLaubenfels)

6. Regularized Scalar Operators, Applied Mathematics Letters, volume 10 (1) 1997. (With R. deLaubenfels and H. Emamirad)

7. Semi Spectral Distributions, Integrated and Regularized Semigroups,  Studia Mathematicae 132 1999 pages 151-172. (With R. deLaubenfels)

8. Spectral distributions and some Cauchy problems, Applied Mathematics Letters, 12 (1999) pages 59-64.

9. Oscillatory blow-up in nonlinear second order ODE’s: the critical case, avec M. Balabane and Ph. Souplet, Discrete and Continuous Dynamical Systems, to appear.

10. A generalization of Gelfand's theorem, Funktionalanalysis und Differentialgleichungen, Helft 6 (2001) pages 184-189.

11. Spectral distribution and Gelfand theorem, submitted to Taiwanese J. of Math. 2002.

12. Periodic and almost periodic solutions for non-dense differential equations, submitted to J. of Dynamic systems and applications ( 2002) avec Kh. Ezzinbi.

13. Numerical study of an alternative method of fictitious domains technique with S. Younan. Submitted to Mathematical models and methods in applied sciences (2002).
 

Preprints

14. On spectral decomposition of unbounded operators and Gelfand's theorem,> avec A. Dirouich et O. ElMennaoui.

15. A dynamical system approach to the construction of singular solutions of  some degenrate elliptic equations, with J. Huentutripay and L. Véron.

16. Asymptotic behavior some functional differential equations, with Kh. Ezzinbi.

17. Asymptotic behavior of solutions for inhomogeneuous non dense differential equations with delay, with Kh. Ezzinbi.

18. Global existence and asymptotic behavior of semi linear heat equations of non local type, with A. ElSoufi and R. Monneau.

In preparation

• Singular solutions of a nonlinear degenerate elliptic equation, part II, with L. Véron.
• Local existence and asymptotic behavior of semi-linear wave equation.
• Qualitative study of some semi-linear parabolic equations with delay, with Kh. Ezzinbi.
• Qualitative study of solutions of fully nonlinear evolution equations.
• Transference principle for groups and H^\infty calculus.

Publication of software of Math.

- STATI1, Les éditions Chrysis, France 1990.
- TRIGO (licence mixte), Les éditions Chrysis, France 1990.
- SMAO6 (licence mixte), Les éditions Chrysis, France 1991.

BOOKS

Building-up mathematics, third year secondary, national manual, life sciences section, Septembre 2000 (with T. Roumi).