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1. About Blow up of Solutions With Arbitrary Positive Initial Energy to Nonlinear Wave Equations (with B.A. Bilgiin)

arXiv:1506.04567 [math AP]

- Preventing blow up by convective terms in dissipative PDE's.
J. Math. Fluid Mech. 18 (2016), no. 3, 463–479.

(with B.A.Bilgin and S.Zelik) arXiv:1509.03845 [math AP] - Attractors for damped quintic wave equations in bounded domains, Annales Henri Poincare , A Journal of Theoretical and Mathematical Physics, Ann. Henri Poincaré 17 (2016), no. 9, 2555–2584. (with A.Savostianov and S. Zelik) arXiv:1309.6272 [math AP]
- Finite-Parameters Feedback Control for
Stabilizing Damped Nonlinear Wave Equations, Contemporary Mathematics,
AMS
**269**(2016)(with E. S. Titi) arXiv:1501.00556 [math AP] - Qualitative properties of solutions for
nonlinear Schroedinger equations with nonlinear boundary conditions on
the half-line, J. Math. Phys.
**57**021511(2016) (with T. Ozsari) arXiv:1508.01043 - A note on a strongly damped wave equation
with fast growing
nonlinearities, J. Math. Phys.
**56**, 011501 (2015)(with S. Zelik) arXiv:1405.2707 [math AP] - Decay of solutions and structural stability
for the coupled Kuramoto-Sivashinsky-Ginzburg-Landau equations,
Applicable Analysis,
**94**(2015) 2342-2354 (with A.O. Celebi) - Infinite-energy solutions for the Cahn-Hilliard equation in cylindrical domains, Mathematical Methods in Applied Scences (Q2),37 , Issue:13 , Pages:1884-1908 , July , 2014, (with A. Eden and S. Zelik) arXiv:1005.3424 [math AP]
- Decay and growth estimates for solutions
of second order
and third order differential - operator equations, Nonlinear Analysis,
Theory Meth. and Appl.
**89**(2013) , 1-7 (with Y. Yilmaz). - Global solvability and blow up for the
convective
Cahn-Hilliard equations with concave potentials, Journal of Math.
Phys.
**54**, 041502 (2013) (with A. Eden and S. Zelik) arXiv:1208.3439 [math AP] - Blow up of solutions to initial boundary value
problem for
quasilinear strongly damped wave equation, J. Math. Anal. Appl.
**403**(2013), no. 1, 89-94 (with B.A. Bilgin). - Counterexamples to regularity of Mane
projections in the
theory
of attractors, Russian Math Surveys,
**68**, 199-226 (with A. Eden and S. Zelik) - Smooth attractors for the Brinkman-Forchheimer
equations with
fast growing nonlinearities,
Comm. Pure and Appl. Anal.
**11**(2012) 2037 - 2054. (with S. Zelk) . arXiv:1101.4070 - Structural stability and decay estimate for
marine riser
equation, Mathematics and Computer Modeling,
**54**(20011), n.11-12, pp 3182-3188 (with O. A. Celebi and S. Gur) - Uniform decay rates for the energy of weakly
damped defocusing
semilinear Schroedinger
equations with inhomogeneous Dirichlet boundary control (with I.
Lasiecka and T. Ozsari),
Journal of Differential Equations ,
**251**(2011) 1841 - 1863 - Global attractors and determining modes for the
3D
Navier-Stokes-Voight equations
(with E. S. Titi) Chin. Ann. Math. Ser. B
**30**(2009), no. 6, 697-714. arXiv:0705.3972 - Finite-Dimensional Attractors for the
Strongly damped
Wave
Equation (with S.Zelik ), Journal of Differential Equations,
**247**(2009) 1120-1155 arXiv:0807.5078 - Global attractors for 2D
Navier-Stokes-Voight
equations
in an unbounded domain
(with A. O. Celebi and M. Polat ), Applicable Analysis,
**88**(2009) 381 - 392 - Gevrey regularity for the attractor of the 3D
Navier-Stokes-Voight equations
(with B. Levant and E. S. Titi) Journal of Nonlinear Science,
**19**(2009) 133 - 152 arXiv:0709.3328 - Structural stability for the double
diffusive convective
Brinkman equations,
(with A.O.Celebi and D.Ugurlu) Applicable Analysis,
**87**(2008) 933 -942 - 3D Convective Cahn-Hilliard Equation,
(with A. Eden)
Comm. Pure Appl. Anal.
**6**(2007) no.4, pp. 1075 -1086 - The convective Cahn-Hilliard equation
(with Alp Eden)
Appl. Math. Lett.,
**20**(2007) no. 4, 455-461 - On continuous dependence on coefficients
of the
Brinkman-Forchheimer equations.
(with A. O. Celebi and D. Ugurlu) Appl. Math. Lett.,
**19**(2006), no. 8, 801-807. - On global behavior of solutions to an
inverse problem
for
nonlinear parabolic equations,
(with A. Eden) J.Math.Anal.Appl.
**307**(2005)120-133 - Continuous dependence for the convective
Brinkman-Forchheimer equations,
(with A. O. Celebi and D. Ugurlu) Appl. Anal, (84)
**9**(2005) 877 - 888. - On global behavior of solutions to an
inverse problem
for
semi-linear hyperbolic equations,
(with A. Eden) Zap. Nauchn. Sem. POMI ,
**318**(2004)120-134 (English Translation in Journal of Math.Sci. July 2006, 136:3718) - The asymptotic behavior of solutions to
an inverse
problem for differential operator equations,
(with A. F. Guvenilir) Math.Comp.Modelling,
**37**(2003) 907-914 - Global solutions of coupled Kuramoto-Sivashinsky and Ginzburg-Landau equations,In :M.S.Birman, St.Hildebrandt, V. A. Solonnikov,N.N.Uraltseva(editors), Nonlinear Problems in Mathematical Physics and Related Topics II. In Honor of Professor O.A.Ladyzhenskaya. Kluwer/Plenum Publishers,2002, pp. 213-227.
- A remark on nonexistence of global
solutions to
quasi-linear hyperbolic
and parabolic equations, (with D. Erdem) Appl. Math. Lett. vol.
**15**(2002) 521-653 - Spatial behavior estimates for the wave
equation under
nonlinear boundary conditions,
(with A. O. Celebi ) Math. Comp. Modelling,
**34**(2001)527-532 - Determining functionals for nonlinear damped wave equations, (with Chueshov I. D.) Math. Phys. Anal. Geom. 8 (2001)215-227.
- Global solution of coupled
Kuramoto-Sivashinsky and
Ginzburg-Landau equations,
Trans. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci.
**20**(2000), no.1, Math. Mech., pp.50-54 - Dictionary of Mathematical Terms , (with H.H.Hacisalihoglu, A.Haciyev, L.M.Brown,A.Sabuncuoglu) Turkish Language Council, Ankara, 2000, 678 pages.
- Attractors for the Generalized Benjamin- Bona -Mahony Equation, (with O.Celebi ,M.Polat ) Journal of Differential Equations, 1999,vol.157, pp. 439 - 451.
- On the Discrete Squeezing Property for Semi-linear Wave Equations, (with A.Eden ) Turkish Journal of Mathematics,1998,vol. 22, no.3, pp.335-341
- A remark on two constructions of exponential attractors for a-contractions (with A.Eden and C.Foias) Journal of Dynamics and Diff.Eq.,1998, vol.10,no.1,pp.37-45
- Phragmen-Lindelof type theorems for some semi-linear elliptic and parabolic equations, (with O.Celebi and F.Tahamtani) Demonstratio Mathematica,1998, vol.31, no.1,pp.43-54
- The long-time behavior of solutions of a nonlinear fourth order equation describing the dynamics of marine riser, (with A.Kurt ) Z.angew.Math.Mech. 77 (1997) 3, pp.209-215
- Blow-up theorems for second order nonlinear evolutionary equations, in O. Boratav, A.Eden, A.Erzan( Eds.) "Turbulence modeling and vortex dynamics" Lecture Not. in Physics, Springer Verlag , 1997, pp.169-181
- On the stability results for third order differential-operator equations, ( with A.Tiryaki) Turkish Journal of Mathematics, 1997, v.21, no.2, pp.179-186.
- Finite dimensional attractors for a class of semi-linear wave equations, ( with A.Eden) Turkish Journal of Mathematics, 1996, v.20, pp. 425-450.
- Global nonexistence of solutions of multi-component diffusion systems, (with D.Erdem) in "Trans. of the Institute of Math. and Mech. of Azerbaijan AS, 1996, vol.6, pp.21-29
- Phragmen-Lindelof principle for a class of fourth-order nonlinear elliptic equations, Bull.Iranian Math.Soc. 20(1994), pp.41-52.
- On minimal global attractor for the phase-field
equations,
Zap. Nauchn.Sem.. Leningrad Otd.. Mat. Inst. Steklov, 1991, v.188,
no.22,pp.70-86 (English Translation in
Journal of
Math. Sci,
**70**(1994), pp 1767-1777) - Global properties of solutions of Caginalp system, Reports of seminar on differential equations and mathematical physics, Baku, 1990, pp.18-19
- On the collapse of solutions of systems of nonlinear equations of parabolic-hyperbolic type (Russian) Izv. Akad. Nauk Azerbaidzhan. SSR Ser. Fiz.-Tekhn. Mat. Nauk 10 (1989), no. 2-3, 33-37
- Global behavior of solutions of nonlinear equations of mathematical physics of classical and non-classical types Post Doct.Thesis,1988, 1988, Leningrad Department of Steklov Math.Inst., Leningrad (St.Petersburg), 213 pages
- Global behavior of solutions to some fourth-order nonlinear equations Zap. Nauchn. Sem.Leningrad Otd.. Mat. Inst. Steklov 1987, v.1163,no.19,pp.66-75. (English Translation in J Math Sci (1990) 49: 1160. 1-7)
- Global behavior of solutions to the Cauchy problem for second order operator-differential equations, Izv. AN.Azerb.SSR ser.fiz.tech.mat.nauk, 1987, v.8, no.6, pp. 28-34.
- Global behavior of solutions of initial boundary value problem for a class of systems of nonlinear equations, Izv. AN Azerb.SSR ser.fiz. tech. mat.nauk, 1987, v.8, no.2, pp. 47-51.
- Estimates of solutions of quasi-linear parabolic equations in unbounded domains, Izv.AN Azerb SSR ser. fiz.tech.mat.nauk, 1986, v.7, no.1, pp. 33-37
- Attractors for some nonlinear problems of mathematical physics , Zap. Nauchn. Sem. Leningrad Otd. Mat. Inst. Steklov 1986, v.182, pp.50-54. (English transl. in J. Sov. Math., 1988, v.40., pp.619-622)
- Collapse of the solutions of parabolic and hyperbolic equations with nonlinear boundary conditions, Zap. Nauchn. Sem. Leningrad Otd. Mat. Inst. Steklov 1983, v.127, pp.75-83 (English transl. in J. Sov. Math., 1984, v.27., pp.1139-1153)
- Theorems of Phragmen-Lindelof type for two nonlinear problems of mechanics, Zap. Nauchn. Sem. Leningrad Otd.Mat.Inst.Steklov, 1981, v.110, no.13, pp.53-56.
- Determination of solutions of the first boundary value problem for a system of Karman equations having an unbounded energy integral, Zap.Nauchn. Sem. Leningrad Otd.Mat.Inst.Steklov 1980, v.96, pp.97-100 (English transl. in J.Sov.Math., 1983, v.21., pp.711-714)
- On stabilisation of solutions of some quasi-linear parabolic equations, (with O.A.Ladyzhenskaya ) Sibirski Mat.Zhurnal, 1978, v.19, no.5, pp.1043-1052 (English transl. in Sibirian Math J., 1978)
- The occurrence of collapse for quasi-linear equations of parabolic and hyperbolic type, (with O.A.Ladyzhenskaya )Zap.Nauchn. Sem. Leningrad Otd.Mat.Inst.Steklov1977, v.69, pp.77-102 (English transl. in J. Sov. Math., 1978, v.10., pp.53-70)
- On mixed problem for semi-linear parabolic-hyperbolic system of equations, Doklady AN Azerb. SSR , 1974, v.30, no.3, pp.20-25
- An investigation of the mixed problem for a certain class of nonstationary systems, Dokl. Akad. Nauk. Azerb. SSR,30 (1974), no. 1, pp.8-11.
- Investigation of generalized solutions of mixed problem for the system of two equations, of parabolic and hyperbolic type, Uch.. Zap.Azerb.Gos. Univ., ser.fiz.mat. nauk, 1972, no.4, pp. 50-58

- Matematik Terimleri Sozlugu, Turk Dil Kurumu, Ankara ,2000 , 678 pp (with H. H. Hacisalihoglu, A. Haciyev, A. Sabuncuoglu, L. M. Brown, E. Ibikli, S. Brown)