Varga K. Kalantarov



PREPRINTS

  1. Remembering Olga Ladyzhenskaya [pdf]
  2. Determining functionals and finite-dimensional reduction for dissipative PDEs revisited. arXiv:2111.04125 (with A. Kostianko and S. Zelik)
  3. Corrigendum to "Blow up of solutions to the initial boundary value problem for quasilinear strongly damped wave equations" [pdf]
    (with B. A. Bilgin)

SELECTED PUBLISHED PAPERS

  1. Determining functionals and finite-dimensional reduction for dissipative PDEs revisited. Journal of Differential Equations, 345 (2023), 78-103 (with A. Kostienko and S. Zelik)
  2. On blow up of solutions of coupled systems of parabolic and hyperbolic equations. Math. Notes, 112:3 (2022), 406411 (with J. Kalantarova)
  3. Finite-parameter feedback stabilization of original Burgers' equations and Burgers' equation with nonlocal nonlinearites, Mathematical Methods in Applied Sciences,2021 (https://doi.org/10.1002/mma.7792), arXiv:1912.05838 [pdf] (with S. Gumus)
  4. Chevron Pattern Equations: Exponential Attractor and Global Stabilization. Vietnam J. Math. 49 (2021), no. 3, 901-918.(with H. Kalantarova & O. Vantzos)
  5. Asymptotic regularity and attractors for slightly compressible Brinkman - Forchheimer equations, Applied Mathematics and Optimization, 2021 ( arXiv:2006.08382) [pdf] (with S. Zelik )
  6. Global Behavior of Solutions to Chevron Pattern Equations, J. Math. Phys. 61 (2020), no. 6, 061511, 13pp (with H. Kalantarova and O. Vantzos)
  7. Blow-up Solutions of Helmholtz Equation for a Kerr Slab with a Complex Linear and Nonlinear Permittivity, J. Math. Phys. 60, 043508 (2019) (with A. Mostafazadeh and N. Oflaz)
  8. Global stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers, Discrete Contin. Dyn. Syst. Ser. B 23 (2018), no. 3, 1325-1345 (with E. S. Titi)
  9. Existence of an attractor and determining modes for structurally damped nonlinear wave equations, Physica D, Nonlinear Phenomena, 376-377 (2018) 15-22 (with B. A. Bilgin)
  10. Non-existence of global solutions to nonlinear wave equations with positive initial energy, Communications on Pure and Applied Analysis, 17 (3) (2018) 987-999 (with B. A. Bilgin)
  11. Determining functionals for damped nonlinear wave equations, Complex Variables and Elliptic Equations, 63 (2018) 931-944 (with B. A. Bilgin)
  12. On the stability of solutions of generalised pipe equation under nonhomogeneous Dirichlet boundary control, Appl. Comp. Math., (2018), 17(1), 48-55 (with M. Meyvaci)
  13. Preventing Blow up by Convective Terms in Dissipative PDE's, J. Math. Fluid Mech., 18, 463-479 (2016) (with B. A. Bilgin and S. Zelik) arXiv:1509.03845 [math AP]
  14. Attractors for damped quintic wave equations in bounded domains, Ann. Henri Poincare 17 (2016), no. 9, 2555-2584 (with A. Savostianov and S. Zelik) arXiv:1309.6272 [math AP]
  15. Finite-Parameters Feedback Control for Stabilizing Damped Nonlinear Wave Equations, Contemporary Mathematics, AMS 269 (2016) (with E. S. Titi) arXiv:1501.00556 [math AP]
  16. 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 [math AP]
  17. A note on a strongly damped wave equation with fast growing nonlinearities, J. Math. Phys. 56 (2015), no. 1, 011501, (with S. Zelik) arXiv:1405.2707 [math AP]
  18. Decay of solutions and structural stability for the coupled Kuramoto-Sivashinsky-Ginzburg-Landau equations, Appl. Anal. 94 (2015), no. 11, 2342€“2354. (with A. O. Celebi)
  19. Infinite-energy solutions for the Cahn-Hilliard equation in cylindrical domains, Mathematical Methods in Applied Sciences, 37 (13), Pages:1884-1908, July 2014, (with A. Eden and S. Zelik) arXiv:1005.3424 [math AP]
  20. 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).
  21. Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials, J. Math. Phys. 54 (2013), no. 4, 041502 (with A. Eden and S. Zelik) arXiv:1208.3439 [math AP]
  22. 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).
  23. Counterexamples to regularity of Mane projections in the theory of attractors, Russian Math Surveys, 68 (2013), no. 2, 199-226 (with A. Eden and S. Zelik)
  24. 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 [math AP]
  25. Structural stability and decay estimate for marine riser equations, Mathematics and Computer Modeling, 54 (2011), n. 11-12, pp 3182-3188 (with O. A. Celebi and S. Gur)
  26. Uniform decay rates for the energy of weakly damped defocusing semilinear Schroedinger equations with inhomogeneous Dirichlet boundary control, Journal of Differential Equations, 251 (2011) 1841-1863 (with I. Lasiecka and T. Ozsari)
  27. Global attractors and determining modes for the 3D Navier-Stokes-Voight equations. Chin. Ann. Math. Ser. B 30, 697 (2009) (with E. S. Titi) arXiv:0705.3972 [math AP]
  28. Finite-dimensional attractors for the quasi-linear strongly damped wave equation, Journal of Differential Equations, 247, 4 (2009), 1120-1155 (with S.Zelik) arXiv:0807.5078 [math AP]
  29. 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
  30. Gevrey regularity for the attractor of the 3D Navier-Stokes-Voight equations Journal of Nonlinear Science, 19 (2009), 133-152 (with B. Levant and E. S. Titi) arXiv:0709.3328 [math AP]
  31. Structural stability for the double diffusive convective Brinkman equations, Applicable Analysis, 87 (2008), 933-942 (with A.O.Celebi and D.Ugurlu)
  32. 3D Convective Cahn-Hilliard Equation, Comm. Pure Appl. Anal. 6 (2007) no. 4, pp. 1075-1086 (with A. Eden)
  33. The convective Cahn-Hilliard equation, Appl. Math. Lett., 20 (2007) no. 4, 455-461 (with A. Eden)
  34. On continuous dependence on coefficients of the Brinkman-Forchheimer equations. Appl. Math. Lett., 19 (2006), no. 8, 801-807. (with A. O. Celebi and D. Ugurlu)
  35. On global behavior of solutions to an inverse problem for nonlinear parabolic equations, J. Math. Anal. Appl. 307 (2005), no.1, 120-133 (with A. Eden)
  36. Continuous dependence for the convective Brinkman-Forchheimer equations, Appl. Anal, 84 (2005), n. 9, 877-888. (with A. O. Celebi and D. Ugurlu)
  37. On global behavior of solutions to an inverse problem for semi-linear hyperbolic equations, (with A. Eden) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 318 (2004) 120-134. English translation in J Math Sci 136, 3718 (2006))
  38. The asymptotic behavior of solutions to an inverse problem for differential operator equations, (with A. F. Guvenilir) Math. Comp. Modelling, 37 (2003) 907-914
  39. 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.
  40. 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
  41. Spatial behavior estimates for the wave equation under nonlinear boundary conditions, (with A. O. Celebi) Math. Comp. Modelling, 34 (2001), 527-532
  42. Determining functionals for nonlinear damped wave equations, (with Chueshov I. D.) Mat. Fiz. Anal. Geom. 8 (2001), p. 215-227.
  43. 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
  44. Dictionary of Mathematical Terms, (with H. H. Hacisalihoglu, A. Haciyev, L. M. Brown, A. Sabuncuoglu) Turkish Language Council, Ankara, 2000, 678 pages.
  45. Attractors for the Generalized Benjamin-Bona-Mahony Equation, (with O. Celebi, M. Polat ) Journal of Differential Equations, 1999, vol. 157, pp. 439-451.
  46. 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
  47. 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
  48. 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
  49. The long-time behavior of solutions of a nonlinear fourth order wave equation, describing the dynamics of marine risers, (with A. Kurt) Z. Angew. Math. Mech. 77 (1997), no. 3, 209-215.
  50. 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
  51. 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.
  52. Finite dimensional attractors for a class of semi-linear wave equations, (with A. Eden) Turkish Journal of Mathematics, 1996, v.20, pp. 425-450.
  53. 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
  54. Phragmen-Lindelof principle for a class of fourth-order nonlinear elliptic equations, (with F. Tahamtani) Bull. Iranian Math. Soc. 20 (1994), no. 2, 41-52.
  55. On the minimal global attractor of a system of phase field equations. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov., 1991, v. 188, no. 22, pp. 70-86. English Translation in J. Math. Sci., 70, 1767-1777 (1994)
  56. Global properties of solutions of Caginalp system, Reports of seminar on differential equations and mathematical physics, Baku, 1990, pp. 18-19
  57. 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
  58. 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.
  59. Global behavior of the solutions of certain 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 49, 1160-1166 (1990).
  60. 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.
  61. 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.
  62. 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
  63. Attractors for some nonlinear problems of mathematical physics, Zap. Nauchn. Sem. Leningrad Otd. Mat. Inst. Steklov 1986, v. 152, pp. 50-54. English translation in J. Soviet Math. 40 (1988), no. 5, 619-622
  64. 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 translation in J Math Sci 27, 2601-2606 (1984)
  65. 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. English translation in J Math Sci 25, 832€“835 (1984)
  66. Determination of the 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 translation in J Math Sci 21, 711€“714 (1983)
  67. Stabilization of the solutions of a certain class of quasilinear parabolic equations as t → ∞, (with O. A. Ladyzhenskaya) Sibirsk. Mat. Zh. 19 (1978), no. 5, 1043-1052, 1214. English translation in Sib Math J 19, 737€“744 (1978)
  68. The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types, (with O.A.Ladyzhenskaya) Zap. Nauchn. Sem. Leningrad Otd. Mat. Inst. Steklov 1977, v.69, pp.77-102. English translation in J. Sov. Math., 1978, v. 10., pp. 53-70
  69. On mixed problem for semi-linear parabolic-hyperbolic system of equations, Doklady AN Azerb. SSR, 1974, v. 30, no. 3, pp. 20-25
  70. 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.
  71. 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

BOOKS

  1. 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)