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Uniwersytet Śląski w Katowicach

asa
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Instytut Matematyki

prof. dr hab. Tomasz Dłotko

profesor Tomasz Dłotko
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Profesor

Pracownicy badawczo-dydaktyczni

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(32) 359 11 75

tomasz.dlotko@us.edu.pl

0000-0003-4294-0503

 

Pełnione funkcje Pełnione funkcje

Członek Rady Naukowej Instytutu Matematyki

CV CV

Data i miejsce urodzenia 

27.10.1955, Katowice.

Wykształcenie

Magisterium: Uniwersytet Śląski w Katowicach, Katowice, 1978,

Doktorat: Uniwersytet Jagielloński, Kraków, 1980,

Habilitacja: Uniwersytet Jagielloński, Kraków, 1987,

Profesura: 1999.

Pełnione funkcje

Wicedyrektor Instytutu Matematyki UŚ w latach 1999-2002 i 2008-2012.

Aktualne zatrudnienie

Instytut Matematyki, Uniwersytet Śląski w Katowicach.

Profesor wizytujący

  • The University of Tennessee, Knoxville (1989);
  • Georgia Institute of Technology, Atlanta (1990);
  • The University of Queensland, Brisbane (1995);
  • Universidade de Sao Paulo, Sao Carlos (1996, 2001, 2007 and 2013);
  • Lanzhou University, China (2008, 2011, 2018);
  • Nanjing University, China (2011).
Plan zajęć Plan zajęć

Mój plan zajęć dostępny jest tej stronie.

Publikacje Publikacje

Artykuły naukowe

  1. The first boundary value problem for a singular linear equation of parabolic type, Prace Mat. UŚ 9, 1979, 46-52.
  2. On singular non-linear parabolic differential inequalities in unbounded domain, Annal. Polon. Math. 37, 1980, 283-287.
  3. Asymptotic behaviour of solutions of the nonlinear heat equation, Annal. Polon. Math. 48, 1988, 109-119.
  4. The one-dimensional Burgers’ equation; existence, uniqueness and stability, Zeszyty Nauk. Univ. Jagiello. 23, 1982, 157-172.
  5. The classical solution of the one-dimensional Burgers’ equation, Zeszyty Nauk. Univ. Jagiello. 23, 1982, 173-182.
  6. Some remarks concerning the one-dimensional Burgers’ equation, Annales Mathematicae Silesianae 4 (16), 1990, 14-24.
  7. The two-dimensional Burgers’ turbulence model, J. Math. Kyoto Univ. 21, 4, 1981, 809-823.
  8. On the Tjon-Wu representation of the Boltzmann equation, Annal. Polon. Math. 42, 1983, 73-82, with A.Lasota.
  9. Stability of the Chandrasekhar-Munch equation, Univ. Jagellon. Acta Math. 28, 1989, 85-92.
  10. Stability of non-linear parabolic equations with dominant main part, Demonstratio Math. 19,I, 1986, 123-137.
  11. Remarks on global bounds of solutions of parabolic equations in divergence form, Rocky Mountain J. Math. 17,3, 1987, 499-510.
  12. Global solutions of reaction-diffusion equations, Funkcial. Ekvac. 30,1, 1987, 31-43.
  13. Decay properties of global solutions of reaction-diffusion equations, Funkcial. Ekvac. 30,1, 1987, 111-114.
  14. Parabolic Equations in Divergence Form. Theory of Global Solutions, Wydawnictwo Uniwersytetu Śląskiego, Katowice, 1987.
  15. A priori estimates for a Navier-Stokes like system, Riv. Mat. Univ. Parma 13 (4), 1987, 187-199.
  16. Parabolic equation modelling diffusion with strong absorption, Atti Sem. Mat. Fis. Univ. Modena 38, 1990, 61-70.
  17. An Lpapproach to a parabolic problem with blowing-up solutions, Demonstratio Math. 22,4, 1989, 1169-1182.
  18. Examples of parabolic problems with blowing-up derivatives, J. Math. Anal. Appl. 154,1, 1991, 226-237.
  19. Local solvability of semilinear parabolic equations, Hokkaido Math. Journal 20, 1991, 481-496.
  20. Local solvability of diagonal semilinear parabolic systems, Czechoslovak Math. Journal 41 (116), 1991, 634-640.
  21. Blow-up of derivatives for parabolic problems, in: Workshop on Partial Differential Equations, B. Kawohl (Ed.), Georgia Institute of Technology, May 1990.
  22. Singular limit in a parabolic equation, Demonstratio Math. 26,2, 1993, 473-481.
  23. Fourth order quasilinear parabolic equations, Tsukuba J. Math. 16,2, 1992, 389-405.
  24. Global attractor for the Cahn-Hilliard equation in H2 and H3J. Differential Equations 113, 1994, 381-393.
  25. Smooth global attractor for the Cahn-Hilliard equation, Differential Equations Dynam. Systems 1,2, 1993, 137-144.
  26. Global attractor for the Cahn-Hilliard system, Bull. Austral. Math. Soc. 49, 1994, 277-293, with J.W. Cholewa.
  27. Global solutions via partial information and the Cahn-Hilliard equation, in: Singularities and Differential Equations, Banach Center Publications, Vol. 33, PWN, Warsaw, 1996, pp. 39-50, with J.W. Cholewa.
  28. Global attractor for sectorial evolutionary equation, J. Differential Equations 125, 1996, 27-39, with J.W. Cholewa.
  29. Global attractors for parabolic p.d.e.’s in Holder spaces, Tsukuba J. Math., 21 (2), 1997, 263-283, with J.W. Cholewa.
  30. Examples of global attractors in parabolic problems, Hokkaido Math. Journal, 27 (1), 1998, 77-103, with A.N. Carvalho, J.W. Cholewa.
  31. Local attractor for n-D Navier-Stokes system, Hiroshima Math. J. 28, 1998, 309-319, with J.W. Cholewa.
  32. Parabolic problems in H1 with fast growing nonlinearities, Nonlinear Analysis TMA 33, 1998, 391-399, with A.N. Carvalho.
  33. Upper semicontinuity of attractors and synchronization, J. Math. Anal. Appl. 220, 1998, 13-41, with A.N. Carvalho, H.M. Rodriguez.
  34. Cauchy problem with subcritical nonlinearity, J. Math. Anal. Appl. 210, 1997, 531-548, with J.W. Cholewa.
  35. Global attractors for problems with monotone operators, Boll. Unione Mat. Ital. II-B (3), 1999, 693-706, with A.N. Carvalho, J.W. Cholewa.
  36. Abstract parabolic problems with non-Lipschitz nonlinearity, in: Evolution Equations: Existence, Regularity and Singularities, Banach Center Publications, Vol. 52, PWN, Warsaw, 2000, 73-81, with J.W. Cholewa.
  37. Remarks on the powers of elliptic operators, Rev. Mat. Complut. 13, 2000, 1-12, with J.W. Cholewa.
  38. Asymptotics of pseudodifferential parabolic equations, Demonstratio Math. 35, 2002, 75-91, with J.W. Cholewa and A.W. Turski.
  39. Abstract parabolic problems in ordered Banach spaces, Colloq. Math. 90, 2001, 1-17, with A.N. Carvalho, J.W. Cholewa.
  40. Bi-spaces global attractors in abstract parabolic equations, in: Banach Center Publications, Vol. 60, PWN, Warszawa 2003, 13-26, with J.W. Cholewa.
  41. Parabolic equations with critical nonlinearities, Topol. Methods Nonlinear Anal. 21, 2003, 311-324, with J.W Cholewa.
  42. Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains, Nonlinear Analysis TMA 56, 2004, 511-554, with J.M. Arrieta, J.W. Cholewa and A. Rodriguez-Bernal.
  43. Cauchy problems in weighted Lebesgue spaces, Czechoslovak Math. J. 54, 2004, 991-1013, with J.W. Cholewa.
  44. Partly dissipative systems in uniformly local spaces, Colloq. Math. 100, 2004, 221-242, with A.N. Carvalho.
  45. Linear parabolic equations in locally uniform spaces, Math. Models Methods Appl. Sci. 14, 2004, 253-294, with J.M. Arrieta, J.W. Cholewa and A. Rodriguez-Bernal.
  46. Hyperbolic equations in uniform spaces, Bull. Acad. Polon. Sci. 52, 2004, 249-263, with J.W. Cholewa.
  47. Strongly damped wave equation in locally uniform spaces, Nonlinear Analysis TMA 64, 2006, 147-187, with J.W. Cholewa.
  48. Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equation, J. Dynam. Differential Equations 18, 2006, 767-814, with S.M. Bruschi, A.N. Carvalho, J.W. Cholewa.
  49. Dissipative parabolic equations in locally uniform spaces, Math. Nachr. 280, 2007, 1643-1663, with J.M. Arrieta, J.W. Cholewa and A. Rodriguez-Bernal.
  50. Semilinear Cauchy problems with almost sectorial operators, Bull. Acad. Polon. Sci. Math. 55, 2007, 333-346.
  51. Strongly damped wave problems: bootstrapping and regularity of solutions, J. Differential Equations 244, 2008, 2310-2333, with A.N. Carvalho, J.W. Cholewa.
  52. Dynamics of the viscous Cahn-Hilliard equation, J. Math. Anal. Appl. 344, 2008, 703-725, with A.N. Carvalho.
  53. Non-autonomous semilinear evolution equations with almost sectorial operators, J. Evol. Equ., 2008, 1-29, with A.N. Carvalho, Marcelo J.D. Nascimento.
  54. Damped wave equations with fast growing dissipative nonlinearities, Discrete Contin. Dyn. Syst. 24, 2009, 1147-1165, with A.N. Carvalho, J.W. Cholewa.
  55. Generalized Korteweg-de Vries equation in H1(R), Nonlinear Analysis TMA 71, 2009, 3934-3947, with M. B. Kania, Meihua Yang.
  56. Dynamics of the modified viscous Cahn-Hilliard equation in RN, Topol. Methods Nonlinear Anal. 35, 2010, 277-294; with Chunyou Sun.
  57. The generalized Korteweg-de Vries-Burgers equation in H2(R), Nonlinear Analysis TMA, 74, 2011, 721-732.
  58. Asymptotic behavior of the generalized Korteweg-de Vries-Burgers equation, J. Evol. Equ. 10, 2010, 571-595; with Chunyou Sun.
  59. Equi-exponential attraction and rate of convergence of attractors with application to a perturbed damped wave equation, Proc. Roy. Soc. Edinburgh Sect. A 144, 2014, 13-51 ; with A.N. Carvalho, J.W. Cholewa.
  60. Analysis of the viscous Cahn-Hilliard equation in RN, J. Differential Equations 252, 2012, 2771-2791; with M. B. Kania, Chunyou Sun.
  61. Pseudodifferential parabolic equations; two examples, Topol. Methods Nonlinear Anal. 43, 2014, 463-492; with M. B. Kania, Chunyou Sun.
  62. Korteweg-de Vries-Burgers system in RN, J. Math. Anal. Appl. 411, 2014, 853-872; with M. B. Kania, Shan Ma.
  63. Pseudodifferential parabolic equations in uniform spaces, Applicable Anal. 93, 2014, 14-34; with M. B. Kania, Chunyou Sun.
  64. Subcritical Hamilton-Jacobi fractional equation in RN, Math. Methods Appl. Sci. 38, 2015, 2547-2560; with M. B. Kania.
  65. Quasi-geostrophic equation in R2, J. Differential Equations 259, 2015, 531-561; with M.B. Kania and Chunyou Sun.
  66. Navier-Stokes equation and its fractional approximations, Appl. Math. Optim. 77, 2018, 99-128 (former title; New look at the Navier-Stokes equation).
  67. Fractional Schrödinger equation; solvability and connection with classical Schrödinger equation, J. Math. Anal. Appl. 457, 2018, 336-360;
    with Flank D. M. Bezerra, Alexandre N. Carvalho, Marcelo J. D. Nascimento.
  68. Fractional Navier-Stokes equation, Discrete Contin. Dyn. Syst. Ser. B 23, 2018, 2967-2988 ; with J.W. Cholewa.
  69. 2D Quasi-geostrophic equation; subcritical and critical cases, Nonlinear Analysis 150, 2017, 38-60; with Chunyou Sun.
  70. A note on the 3-D Navier-Stokes equations, Topol. Methods Nonlinear Anal. 52, 2018, 195-212; with J.W. Cholewa.
  71. Critical and super-critical abstract parabolic equations, Discrete Contin. Dyn. Syst. Ser. B 25, 2020, 1517-1541; with Tongtong Liang, Yejuan Wang.
  72. Dirichlet problem for critical 2D quasi-geostrophic equation with large data, submitted 30.03.2020; with Tongtong Liang, Yejuan Wang.

Materiały konferencyjne

  1. Statistical stability and the lower bound function technique, in: Pitman Research Notes 141, Proc. Autumn Course on Semigroups, Theory and Applications, Trieste 1984, pp. 75-95, with A.Lasota.
  2. Global description of divergence quasilinear parabolic equations, in: Proc. 4-th Conf. Funct.-Diff. Equations 1985, M.Kisielewicz (Ed.), pp. 25-34.
  3. Blow-up of derivatives for parabolic problems, in: Workshop on Partial Differential Equations, B. Kawohl (Ed.), Georgia Institute of Technology, May 1990.

 Monografie

  1. Global Attractors in Abstract Parabolic Problems, Cambridge University Press, Cambridge, 2000, with J.W. Cholewa; ISBN 978-0-521-79424-4.
  2. Critical Parabolic-Type Problemsde Gruyter Series in Nonlinear Analysis and Applications 34, Berlin/Boston, 2020, with Yejuan Wang;  ISBN 978-3-11-059755-4.
Okładka książki: T. Dłotko, Y. Wang, Critical Parabolic-type Problemu

Okładka i strona tytułowa książki: T. Dłotko, Y. Wang, Global Attractors in Abstract Parabolic Problems

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