1. Linear operators.
2. Semigroups of bounded operators.
3. Fractional powers of positive operators.
4. Abstract parabolic equations.
5. Examples and applications.
[21] (with Tomasz Dłotko) Evolution equations with sectorial operator on fractional powers scales, Applied Mathematics & Optimization 88, Article number: 43 (2023), 41 pages. [PDF]
[20] (with Maria Kania) Exponential attractors for modified Swift-Hohenberg equation in RN, Differential and Integral Equations 36 (5-6) (2023), 347-366. [Preprint]
[19] (with Maria Kania) Dissipative mechanism and global attractor for modified Swift-Hohenberg equation in RN, Turkish Journal of Mathematics 46 (7) (2022), 2728-2750. [PDF][18] Pullback attractors via quasi-stability for non-autonomous lattice dynamical systems, Discrete and Continuous Dynamical Systems Series B 27 (9) (2022), 5317-5342.
[17] (with Tomasz Dłotko) Comprehensive description of solutions to semilinear sectorial equations: an overview, Nonlinear Dynamics and Systems Theory 22 (1) (2022), 21–45. [PDF]
[16] (with Jan Cholewa) On fractal dimension of global and exponential attractors for dissipative higher order parabolic problems in RN with general potential, in Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics, Springer, Understanding Complex Systems, 2021, ISBN 978-3-030-50301-7, pp. 293-314.
[15] (with Jan Cholewa) Lattice dynamical systems: dissipative mechanism and fractal dimension of global and exponential attractors, J. Evol. Equ. 20 (2020), 485–515. [PDF]
[14] (with Waldyr M. Oliva, Carlos Rocha) On a definition of Morse-Smale evolution processes, Discrete Contin. Dyn. Syst. 37 (7) (2017), 3601-3623. [PDF][13] (with Pedro Marín-Rubio) Pullback exponential attractors for parabolic equations with dynamical boundary conditions, Taiwanese J. Math., 21 (4) (2017), 819-839. [PDF]
[12] (with Everaldo M. Bonotto, Matheus C. Bortolan, Rodolfo Collegari) Semicontinuity of attractors for impulsive dynamical systems, J. Differential Equations 261 (8) (2016), 4338-4367. [PDF]
[11] (with Everaldo M. Bonotto, Matheus C. Bortolan, Alexandre N. Carvalho) Global attractors for impulsive dynamical systems - a precompact approach, J. Differential Equations 259 (7) (2015), 2602-2625. [PDF]
[10] Pullback exponential attractors with admissible exponential growth in the past, Nonlinear Anal. 104 (2014), 90-108. [PDF]
[09] Bi-space pullback attractors for closed processes, São Paulo J. Math. Sci. 6 (2) (2012), 227-246. [PDF]
[08] (with Messoud Efendiev) Pullback exponential attractors for nonautonomous equations Part II: Applications to reaction-diffusion systems, J. Math. Anal. Appl. 381 (2) (2011), 766-780. [PDF]
[07] (with Messoud Efendiev)
Pullback exponential attractors for nonautonomous equations Part I: Semilinear parabolic problems,
J. Math. Anal. Appl. 381 (2) (2011), 748-765.
[PDF]
[06] (with Carlos Rocha)
Transversality in scalar reaction-diffusion equations on a circle,
J. Differential Equations 245 (3) (2008), 692-721.
[PDF]
[05] (with Messoud Efendiev) A note on attractors with finite fractal dimension, Bull. London Math. Soc. 40 (4) (2008), 651-658.
[04] (with Jan Cholewa, Gianluca Mola) Remarks on the fractal dimension of bi-space global and exponential attractors, Boll. Unione Mat. Ital. (9) 1 (1) (2008), 121-145. [PDF]
[03] Asymptotics of parabolic equations with possible blow-up, Colloquium Mathematicum 99 (1) (2004), 61-73. [PDF]
[02] Dynamically equivalent perturbations of linear parabolic equations, Demonstratio Mathematica 37 (2) (2004), 327-348. [PDF]
[01] Differential Equations with Sectorial Operator, Wydawnictwo Uniwersytetu Śląskiego, Katowice, 2002, ISBN 83-226-1164-1, pp. 120.
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Contents: 1. Linear operators. 2. Semigroups of bounded operators. 3. Fractional powers of positive operators. 4. Abstract parabolic equations. 5. Examples and applications. |