INSTYTUT MATEMATYKI
Uniwersytet Śląski
40-007 Katowice, ul. Bankowa 14

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JAN CHOLEWA – SCIENTIFIC PAPERS

  1. Local solvability of higher order semilinear parabolic equations, Hokkaido Math. J., 21, 1992, 491-508.
  2. Higher dimensional semilinear parabolic problems, Hokkaido Math. J., 22, 1993, 365-371.
  3. Global attractor for the Cahn-Hilliard system, Bull. Austral. Math. Soc. 49, 1994, 277-292, with Tomasz Dlotko.
  4. Local existence of solutions of 2m-th order semilinear parabolic equations, Demonstratio Mathematica, 28, 1995, 929-944.
  5. Global solutions via partial information and the Cahn-Hilliard equation, Singularities and Differential Equations, Banach Center Publications (PWN), Vol. 33, Warszawa, 1996, 39-50, with Tomasz Dlotko.
  6. Global attractor for sectorial evolutionary equation, J. Differential Equations 125, 1996, 27-39, with Tomasz Dlotko.
  7. Global attractors for parabolic p.d.e.'s in Holder spaces, Tsukuba J. Math. 21, 1997, 263-283, with Tomasz Dlotko.
  8. Cauchy problem with subcritical nonlinearity, J. Math. Anal. Appl. 210, 1997, 531-548, with Tomasz Dlotko.
  9. Local attractor for n-D Navier-Stokes system, Hiroshima Math. J., 28, 1998, 309-319, with Tomasz Dlotko.
  10. Examples of global attractors in parabolic problems, Hokkaido Math. J. 27, 1998, 77-103, with A.N. Carvalho and Tomasz Dlotko.
  11. Global attractors for problems with monotone operators, Boll. Un. Math. Ital. Vol. II-B, 3, 1999, 693-706, with A.N. Carvalho and Tomasz Dlotko.
  12. Abstract parabolic problem with non-Lipschitz nonlinearity, in: Evolution Equations: Existence, Regularity and Singularities, Banach Center Publications (PWN), Vol. 52, Warszawa, 2000, 73-81, with Tomasz Dlotko.
  13. Some counterexamples in dissipative systems, Dynam. Contin. Discrete Impuls. Systems. 7, 2000, 159-176, with J. K. Hale.
  14. Remarks on the powers of elliptic operators, Revista Matematica Complutense 13, 2000, 1-12, with Tomasz Dlotko.
  15. Abstract parabolic problems in ordered Banach spaces, Colloq. Math. 90, 2001, 1-17, with A.N. Carvalho and Tomasz Dlotko.
  16. Asymptotics of pseudodifferential parabolic equations, Demonstratio Math. 35, 2002, 75-91, with Tomasz Dlotko and Andrzej Turski.
  17. Local well posedness for strongly damped wave equations with critical nonlinearities, Bulletin of the Australian Mathematical Society, 66, 2002, 443-463, with A. N. Carvalho.
  18. Attractors for strongly damped wave equations with critical nonlinearities, Pacific Journal of Mathematics, 207, 2002, 287-310, with A.N. Carvalho.
  19. Pewne nietypowe własności rozwiązań nieliniowych równań ewolucyjnych, Roczniki Polskiego Towarzystwa Matematycznego, Seria II: Wiadomości Matematyczne XXXVIII, 2002.
  20. Bi-spaces global attractors in abstract parabolic equations, in: Banach Center Publications (PWN) Vol. 60, 2003, 13-26, with Tomasz Dłotko.
  21. Parabolic equations with critical nonlinearities, Topol. Methods Nonlinear Anal. 21, 2003, 311-324, with Tomasz Dlotko.
  22. Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains, Nonlinear Analysis TMA 56, 2004, 511-554, with J.M. Arrieta, Tomasz Dlotko, A. Rodriguez-Bernal.
  23. Linear parabolic equations in locally uniform spaces, Math. Models Methods Appl. Sci. 14, 2004, 253-294, with J.M. Arrieta, Tomasz Dlotko, A. Rodriguez-Bernal.
  24. Cauchy problems in weighted Lebesgue spaces, Czechoslovak Math. J. 54, 2004, 991-1013, with Tomasz Dlotko.
  25. Hyperbolic equations in uniform spaces, Bull. Acad. Polon. Sci. 52, 2004, 249-263, with Tomasz Dlotko.
  26. Continuation and asymptotics of solutions to semilinear parabolic equations with critical nonlinearities, J. Math. Anal. Appl. 310, 2005, 557-578, with A. N. Carvalho.
  27. Strongly damped wave equation in locally uniform spaces, Nonlinear Analysis TMA 64, 2006, 174-187, with Tomasz Dlotko.
  28. Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equation, J. Dynam. Differential Equations 18, 767-814, 2006, with S.M. Bruschi, A.N. Carvalho, Tomasz Dlotko.
  29. From point dissipative to compact dissipative – addendum to “Some counterexamples in dissipative systems”, Dynam. Contin. Discrete Impuls. Systems 14, 2007, 147-164, with J.K. Hale.
  30. Dissipative parabolic equations in locally uniform spaces, Math. Nachr. 280, 2007, 1643-1663, with J.M. Arrieta, Tomasz Dlotko, A. Rodriguez-Bernal.
  31. Strongly damped wave equations in , Discrete and Continuous Dynamical Systems, Supplement 2007, 230-239, with A.N. Carvalho.
  32. Regularity of solutions on the global attractor for a semilinear damped wave equation, J. Math. Anal. Appl. 337, 2008, 932-948, with A.N. Carvalho.
  33. Remarks on the fractal dimension of bi-space global and exponential attractors, Boll. Un. Math. Ital. 1, 2008, 121-145, with R. Czaja, G. Mola.
  34. Strongly damped wave problems: bootstrapping and regularity of solutions, J. Differential Equations 244, 2008, 2310-2333, with A.N. Carvalho, Tomasz Dlotko.
  35. Local well posedness, asymptotic behavior and asymptotic bootstrapping for a class of semilinear evolution equations of the second order in time, Trans. Amer. Math. Soc. 361, 2009, 2567-2586, with A.N. Carvalho.
  36. Damped wave equations with fast growing dissipative nonlinearities, Discrete Contin. Dyn. Syst. 24, 2009, 1147-1165, with A.N. Carvalho, Tomasz Dlotko.
  37. Extremal equilibria for dissipative parabolic equations in locally uniform spaces, Math. Models Methods Appl. Sci. 19, 2009, 1995-2037, with A. Rodriguez-Bernal.
  38. Extremal equilibria for monotone semigroups in ordered spaces with application to evolutionary equations, J. Differential Equations, 249, 2010, 485-525, with A. Rodriguez-Bernal.
  39. Exponential global attractors for semigroups in metric spaces with applications to differential equations, Ergod. Th. & Dynam. Sys., 31, 2011, 1641-1667, with A.N. Carvalho.
  40. Linear and semilinear higher order parabolic equations in R^N, Nonlinear Analysis TMA, 75, 2012, 194-210, with A. Rodriguez-Bernal.
  41. Dissipative mechanism of a semilinear higher order parabolic equation in R^N, Nonlinear Analysis TMA, 75, 2012, 3510-3530, with A. Rodriguez-Bernal.
  42. On the Cahn-Hilliard equation in H^1(R^N), J. Differential Equations 253, 2012, 3678-3726, with A. Rodriguez-Bernal.
  43. Reduction of infinite dimensional systems to finite dimensions: Compact convergence approach, SIAM J. Math. Anal., 45, 2013, 600-638, with A.N. Carvalho, G. Lozada-Cruz, M.R.T. Primo.
  44. Equi-exponential attraction and rate of convergence of attractors with application to a perturbed damped wave equation, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 144, 2014, 13-51, with A.N. Carvalho, Tomasz Dlotko.
  45. Critical and supercritical higher order parabolic problems in R^N, Nonlinear Analysis 104, 2014, 50-74, with A. Rodriguez-Bernal.
  46. A note on the Cahn-Hilliard equation in H1(RN) involving critical exponent, Math. Bohem. 139, 2014, 269-283, with A. Rodriguez-Bernal.
  47. On the continuation of solutions of nonautonomous semilinear parabolic problems, Proceedings of the Edinburgh Mathematical Society, 59, 2016, 17-55, with A.N. Carvalho, M.J.D. Nascimento.
  48. Linear higher order parabolic problems in locally uniform Lebesgue's spaces, J. Math. Anal. Appl., 449, 2017, 1-45, with A. Rodriguez-Bernal.
  49. Parabolic approximation of damped wave equations via fractional powers: fast growing nonlinearities and continuity of the dynamics, J. Math. Anal. Appl., 450, 2017, 377-405, with F. D. M. Bezerra, A. N. Carvalho, M. J. D. Nascimento.
  50. Nonlinear evolution equations in scales of Banach spaces and applications to PDEs, Journal of Abstract Differential Equations and Applications, 8, 2017, 1-69, with C. Quesada, A. Rodriguez-Bernal.
  51. NLS-like equations in bounded domains: parabolic approximation procedure, Discrete Contin. Dyn. Syst. Ser. B, 23, 2018, 57-77, with A.N. Carvalho.
  52. Fractional Navier-Stokes Equations, Discrete Contin. Dyn. Syst. Ser. B, 23, 2018, 2967-2988, with Tomasz Dlotko.
  53. A note on the 3-D Navier-Stokes equations, Topol. Methods Nonlinear Anal., 52, 2018, 195-212, with Tomasz Dlotko.
  54. Lattice dynamical systems: dissipative mechanism and fractal dimension of global and exponential attractors, J. Evol. Equ., doi 10.1007/s00028-019-00535-3, with R. Czaja.

Monograph: Global Attractors in Abstract Parabolic Problems, Cambridge University Press, Cambridge, 2000, with Tomasz Dlotko.

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