Prof. Dr. ALP EDEN

 

CV

 

Publications

BOOKS

 

Exponential Attractors for Dissipative Evolution Equations (with C. Foias, B. Nicolaenko and R. Temam), 1994, Paris, Masson Publications.

 

Proccedings of the Workshop on Turbulence Modelling and Vortex Dynamics (co-editors: A. Erzan and O. Boratav), 1997, Springer-Verlag, Lecture Notes in Physics.

 

ARTICLES

 

1) “Local Lyapunov exponents and a local estimate of Hausdorff dimension”, Attractors, inertial manifolds and their approximation (Marseille-Luminy, 1987). RAIRO Modél. Math. Anal. Numér. 23 (1989), no. 3, 405--413.

 

2) “Explicit Dimension estimates of Attractors for the MHD equations in three dimensional space” Physica D, 40, 338-352, 1989. (with A. Libin)

 

3) “Local estimates for the Hausdorff dimension of an attractor”,  J. Math. Anal. Appl. 150 (1990), no. 1, 100—119.

 

4) “On Burgers’ original Mathematical model of Turbulence”, Nonlinearity, 3, 557-566, 1990.

 

5) “Ensembles inertiels pour des equations d’evolution dissipative”, C.R. Acad. Sci. Paris, 310, Series I, 559-562, 1990. (with C.Foias, B. Nicolaenko and R. Temam)

 

6) “Error analysis of nonlinear evolution equations and associated dynamical systems”,  Appl. Math. Lett. 3 (1990), no. 3, 31--34. (with Michaux, B.; Rakotoson, J.-M.)

 

7) “Semi-discretized non-linear evolution equations as discrete dynamical systems and error analysis”, Indiana Journal of Mathematics, 39, 737-783, 1990. (with B. Michaux and J.M. Rakatoson)

 

8) “A simple proof of the generalized Lieb-Thirring inequalities in one-space dimension”,  J. Math. Anal. Appl. 162 (1991), no. 1, 250--254. (with Foias, C.)

 

9) “ Doubly nonlinear parabolic type equations as dynamical systems” Journal of Dynamics and Differential Equations, 3, 87-131, 1991. (with B. Michaux and J.M. Rakatoson)

 

10) “Local and Global Lyapunov Exponents ”, Journal of Dynamics and Differential Equations, 3, 133-177, 1991. (with C.Foias and R. Temam)

 

11) “Finite-dimensional exponential attractors for semilinear wave equations with damping”, (with Milani, A. J.; Nicolaenko, B.)  J. Math. Anal. Appl. 169 (1992), no. 2, 408-419.

 

12) “Exponential attractors and their relevance to fluid dynamics systems”, Physica D, 63, 350-360, 1993. (with C. Foias, B. Nicolaenko and Z-S. She)

 

13) “Local exponential attractors for models of phase change for compressible gas dynamics”, Nonlinearity, 6,  93-117, 1993. (with A.J. Milani and B. Nicolaenko)

 

14) “Exponential attractors for extensible beam equations”, Nonlinearity, 6, 457-479, 1993. (with A.J. Milani)

 

15) “Hölder continuity for the inverse of Mané’s projection”, Journal of Mathematical Analysis and its Applications, 178, 1, 22-29, 1993. (with A. Ben-Artzi, C. Foias and B. Nicolaenko)

 

16) “ Exponential Attractors of Optimal Lyapunov dimension for Navier-Stokes equations”, Journal of Dynamics and Differential Equations, 6, 2, 310-323, 1994. (with C. Foias and B. Nicolaenko)

 

17) “Exponential attractors for a doubly nonlinear equation”,  J. Math. Anal. Appl. 185 (1994), no. 2, 321--339. (with Rakotoson, J.-M.)

 

18) “On the convergence of attractors and exponential attractors for singularly perturbed hyperbolic equations”, Turkish J. Math. 19 (1995), no. 1, 102-117. (with A.J. Milani)

 

19) “ Finite dimensional attractors for a class of semilinear wave equations”, Turkish Mathematical Journal, 20, 3, 425-450, 1996. (with V. Kalantarov)

 

20) “ A remark on two constructions of exponential attractors for a-contractions”, Journal of Dynamics and Differential Equations, 10, 1, 37-45, 1998. (with C. Foias and V. Kalantarov)

 

21) “On the discrete squeezing property for semilinear wave equations”, Turkish J. Math. 22 (1998), no. 3, 335-341. (with Kalantarov, V. K.)

 

22) “Finite dimensional attractors for a general class of non-autonomous wave equations”, Applied Mathematics Letters, 13, 17-22, 2000. (with V. Kalantarov and A. Miranville)

 

23) “On the asymptotic stability of positive maps on homogeneous lattices”, Turkish Mathematical Journal, 24, 3, 277-281, 2000.

 

24) “Finite Dimensional Dynamics on the Attractors”, in Proceedings of the Third International Palestinian Conference in Mathematics and Mathematics Education, editors: S. Elaydi, E.S.Titi, M. Saleh, S.K. Jain and R. Abu-Saris, World Scientific, 90-97,  2002.

 

25) “On global behaviour  of solutions to an inverse problem for semi-linear hyperbolic equations”, Zapiskii Nauchix Seminarov POMI, 318, 120-133, 2004. (with V. Kalantarov)

 

26) “Global existence and non-existence results for a generalized Davey-Stewartson system”, Journal of Physics A : Mathematics and General, 37, 11531-11546, 2004. (with C. Babaoğlu and S. Erbay)

 

27) “On travelling wave solutions of a generalized Davey-Stewartson system”, IMA Journal of Applied Mathematics, 70, 15-24, 2005. (with S. Erbay)

 

28) “On global behaviour of solutions to an inverse problem for semilinear parabolic equations”, Journal of Mathematical Analysis and its Applications, 307, 120-133, 2005. (with V. Kalantarov)

 

29) “Two remarks on a generalized Davey-Stewartson system”, Nonlinear Analysis, 64, 979-986, 2006. (with H.A. Erbay and G.M. Muslu)

 

30) “Standing Waves for a Generalized Davey-Stewartson system” Journal of Physics A: Mathematics and General, 39 (2006) 13435-13444 (with S. Erbay)

 

31) “On the Global Behaviour of Solutions to Nonlinear Inverse Source problems” to appear in the Proceedings of the Conference on Differential&Difference Equations and Applications, p. 1-12, 2006. (with V. Kalantarov)

 

32) “On Convective Cahn-Hilliard Equation”,  Applied Mathematics Letters, 20 (2007) 455-461  (with V. Kalantarov)

 

33) “Some results on Coupled Linear Wave Equations” submitted (with S. Erbay and I. Hacinliyan)

 

34) “3D Convective Cahn-Hilliard equation” submitted (with V. Kalantarov)

 

MathSciNet Publication Results for “Author=(EDEN, A*)”

 

Education

Ph.D.

Indiana University, Bloomington, Indiana, USA

1989

Mathematics

M.A.

Indiana University, Bloomington, Indiana, USA

1983

Mathematics

B.A.

Bogazici University, Istanbul, Turkey

1981

Mathematics

B.S.

Bogazici University, Istanbul, Turkey

1981

Civil Engineering

 

Areas of Interest

Non-linear Partial Differential Equations, Dynamical Systems,

Finance Mathematics, Mathematical Modelling.

 

Phone Number

90-212-359-6603

 

E-Mail

eden [at] boun.edu.tr