Department of Mathematics

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

• “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.
• “ Explicit Dimension estimates of Attractors for the MHD equations in three dimensional space” Physica D, 40, 338-352, 1989. (with A. Libin)
• “Local estimates for the Hausdorff dimension of an attractor”,  J. Math. Anal. Appl. 150 (1990), no. 1, 100—119.
• “ On Burgers’ original Mathematical model of Turbulence”, Nonlinearity, 3, 557-566, 1990.
• “ 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)
• “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.)
• “ 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)
• “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.)
• “ 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)
• “Local and Global Lyapunov Exponents ” , Journal of Dynamics and Differential Equations, 3, 133-177, 1991. (with C.Foias and R. Temam)
• “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.
• “Exponential attractors and their relevance to fluid dynamics systems”, Physica D, 63, 350-360, 1993. (with C. Foias, B. Nicolaenko and Z-S. She)
• “Local exponential attractors for models of phase change for compressible gas dynamics”, Nonlinearity,6, 93-117, 1993. (with A.J. Milani and B. Nicolaenko)
• “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)
• “ 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)
• “Exponential attractors for a doubly nonlinear equation”,  J. Math. Anal. Appl. 185 (1994), no. 2, 321--339. (with Rakotoson, J.M.)
• “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)
• “ Finite dimensional attractors for a class of semilinear wave equations”, Turkish Mathematical Journal, 20, 3, 425-450, 1996. (with V. Kalantarov)
• “ 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)
• “On the discrete squeezing property for semilinear wave equations”, Turkish J. Math. 22 (1998), no. 3,Kalantarov, V. K.) 335--341.(with
• “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)
• “On the asymptotic stability of positive maps on homogeneous lattices”, Turkish Mathematical Journal, 24, 3, 277-281, 2000.
• “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.
• “ On travelling wave solutions of a generalized Davey-Stewartson system”, IMA Journal of Applied Mathematics, 70, 15-24, 2005. (with S. Erbay)
• “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)
• “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)
• “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)
• “ Two remarks on a generalized Davey-Stewartson system”, Nonlinear Analysis, 64, 979-986, 2006. (with H. A. Erbay and G. M. Muslu)
• “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)
• “ On Convective Cahn-Hilliard Equation”,  Applied Mathematics Letters, 20 (2007) 455-461(with V. Kalantarov)
• “ Standing Waves for a Generalized Davey-Stewartson system” Journal of Physics A: Mathematics and General, 39 (2006) 13435-13444 (with S. Erbay)
• “ Reducing a generalized Davey-Stewartson system to a non-local nonlinear Schrödinger equation”  accepted in Chaos, Solitons and Fractals  (with S. Erbay and I. Hacinliyan)
• “3D Convective Cahn-Hilliard equation” Communications on Pure and Applied Analysis, 6, no.4, December 2007.(with V. Kalantarov)
• “A global existence result for small mass solutions for GDS system”, submitted (with I. Hacinliyan)
• “Closing the gap in the purely elliptic GDS system” Nonlinear Analysis: Theory, Methods and Applications, 69, 2575-2581, 2008. ( with H.A. Erbay and G. Muslu)
• “Standing waves for a Generalized Davey-Stewartson equation: Revisited” Applied Mathematics Letters, 21,342-347, 2008. ( with I. A. Topaloglu)
• “On Almost Cubic NLS equations: Existence, Uniqueness and Scattering”, accepted  to CPAA, (with E. Kuz)
• “On the focusing and defocusing cases of the purely elliptic GDS system”, acccepted  to IMA Journal on  Applied Mathematics , (with E. Kuz and B. Gurel)
• “On the special solutions of the Generalized Davey-Stewartson system”, accepted to Applied Mathematics Letters (with B. Gurel).

Other Publications

• “ On Attractors and Exponential Attractors for some Nonlinear Wave equations with Damping”, VII. Ulusal Matematik Sempozyumu Bildiri Kitabı, 27-40, 1994. (with V. Kalantarov)
• “ Katastrof ve Kaos Teorileri hakkında”, Matematik Dünyası, 6-11, 1994. (in Turkish)
• “Doğru bir Boyut Kavramına Doğru”, XI. Ulusal Matematik Sempozyumu Bildiri Kitabı, 1-12, 1998. (in Turkish)
• “Genelleştirilmiş Davey-Stewartson Sistemi için iki yeni sonuç”, itüdergisi/c, 2007. ( Gülçin M. Muslu ve Hüsnü A. Erbay ile birlikte) (in Turkish)
• “ Zürich İzlenimleri” , Matematik Dünyası, 2007. (in Turkish)
• “Some results on coupled linear wave equations”, PAMM, Proc. Appl. Math.Mech., 7, 2040013-2040014, doi: 10.1002/pamm.200700291 (with Saadet Erbay and  İrma Hacinliyan)