Kostianko, Anna; Zelik, Sergey Smooth extensions for inertial manifolds of semilinear parabolic equations. (English) Zbl 07818637 Anal. PDE 17, No. 2, 499-533 (2024). MSC: 35B40 35B42 37D10 37L25 PDFBibTeX XMLCite \textit{A. Kostianko} and \textit{S. Zelik}, Anal. PDE 17, No. 2, 499--533 (2024; Zbl 07818637) Full Text: DOI arXiv
Zhao, Junyilang; Shen, Jun; Lu, Kening Persistence of \(C^1\) inertial manifolds under small random perturbations. (English) Zbl 07818497 J. Dyn. Differ. Equations 36, No. 1, Suppl., S333-S385 (2024). MSC: 60H15 60H40 35K58 37H10 37L55 35B42 PDFBibTeX XMLCite \textit{J. Zhao} et al., J. Dyn. Differ. Equations 36, No. 1, S333--S385 (2024; Zbl 07818497) Full Text: DOI
Hu, Wenjie; Caraballo, Tomás Pullback exponential attractors with explicit fractal dimensions for non-autonomous partial functional differential equations. (English) Zbl 07797095 J. Nonlinear Sci. 34, No. 1, Paper No. 27, 36 p. (2024). MSC: 37L25 37L30 37L55 37B55 60H15 35R60 PDFBibTeX XMLCite \textit{W. Hu} and \textit{T. Caraballo}, J. Nonlinear Sci. 34, No. 1, Paper No. 27, 36 p. (2024; Zbl 07797095) Full Text: DOI
Bonotto, Everaldo M.; Bortolan, Matheus C.; Pereira, Fabiano Lyapunov functions for dynamically gradient impulsive systems. (English) Zbl 07788943 J. Differ. Equations 384, 279-325 (2024). MSC: 37L05 37L15 37L25 PDFBibTeX XMLCite \textit{E. M. Bonotto} et al., J. Differ. Equations 384, 279--325 (2024; Zbl 07788943) Full Text: DOI
Lee, Jihoon; Pires, Leonardo Structural stability for scalar reaction-diffusion equations. (English) Zbl 07822991 Electron. J. Qual. Theory Differ. Equ. 2023, Paper No. 54, 12 p. (2023). MSC: 37D15 34D30 35B41 35B42 PDFBibTeX XMLCite \textit{J. Lee} and \textit{L. Pires}, Electron. J. Qual. Theory Differ. Equ. 2023, Paper No. 54, 12 p. (2023; Zbl 07822991) Full Text: DOI
Zelik, Sergey V. Attractors. Then and now. (English) Zbl 07794505 Russ. Math. Surv. 78, No. 4, 635-777 (2023); and Usp. Mat. Nauk 78, No. 4, 53-198 (2023). MSC: 35-02 35B41 37L30 PDFBibTeX XMLCite \textit{S. V. Zelik}, Russ. Math. Surv. 78, No. 4, 635--777 (2023; Zbl 07794505) Full Text: DOI arXiv MNR
Kostianko, Anna; Sun, Chunyou; Zelik, Sergey Inertial manifolds for 3D complex Ginzburg-Landau equations with periodic boundary conditions. (English) Zbl 07786032 Indiana Univ. Math. J. 72, No. 6, 2403-2429 (2023). MSC: 35Q56 35Q30 76F20 35B33 35B40 35B42 35B65 35B44 35A01 35A02 35R01 PDFBibTeX XMLCite \textit{A. Kostianko} et al., Indiana Univ. Math. J. 72, No. 6, 2403--2429 (2023; Zbl 07786032) Full Text: DOI arXiv
van den Berg, Jan Bouwe; Jaquette, Jonathan; Mireles James, Jason D. Validated numerical approximation of stable manifolds for parabolic partial differential equations. (English) Zbl 07781550 J. Dyn. Differ. Equations 35, No. 4, 3589-3649 (2023). MSC: 65M15 35B40 35B42 35K55 37L15 37L25 37L65 37M21 68V05 35Q35 PDFBibTeX XMLCite \textit{J. B. van den Berg} et al., J. Dyn. Differ. Equations 35, No. 4, 3589--3649 (2023; Zbl 07781550) Full Text: DOI arXiv
Wang, Rong-Nian; Zhao, Jia-Cheng The 3-D nonlinear hyperbolic-parabolic problems: invariant manifolds. (English) Zbl 07781535 J. Dyn. Differ. Equations 35, No. 4, 3113-3147 (2023). MSC: 35B42 35G61 37L25 PDFBibTeX XMLCite \textit{R.-N. Wang} and \textit{J.-C. Zhao}, J. Dyn. Differ. Equations 35, No. 4, 3113--3147 (2023; Zbl 07781535) Full Text: DOI
Wang, Fengling; Li, Yangrong Mean-square invariant manifolds for stochastic weak-damping wave equations with nonlinear noise. (English) Zbl 07765955 Discrete Contin. Dyn. Syst., Ser. S 16, No. 10, 2649-2671 (2023). Reviewer: Matheus Cheque Bortolan (Florianópolis) MSC: 37L25 37L55 37L15 37H30 37D10 60H15 35B42 35R60 PDFBibTeX XMLCite \textit{F. Wang} and \textit{Y. Li}, Discrete Contin. Dyn. Syst., Ser. S 16, No. 10, 2649--2671 (2023; Zbl 07765955) Full Text: DOI
Wang, Rong-Nian; Wu, Jianhong; Zhao, Jia-Cheng Theory of invariant manifolds for infinite-dimensional nonautonomous dynamical systems and applications. (English) Zbl 07757945 SIAM J. Math. Anal. 55, No. 5, 5386-5431 (2023). MSC: 37L25 37D10 35B40 37C60 PDFBibTeX XMLCite \textit{R.-N. Wang} et al., SIAM J. Math. Anal. 55, No. 5, 5386--5431 (2023; Zbl 07757945) Full Text: DOI
Wang, Rong-Nian; Zhao, Jia-Cheng; Miranville, Alain Hyperdissipative Navier-Stokes equations driven by time-dependent forces: invariant manifolds. (English) Zbl 07674591 SIAM J. Appl. Dyn. Syst. 22, No. 1, 199-234 (2023). MSC: 37L25 76D05 35Q35 PDFBibTeX XMLCite \textit{R.-N. Wang} et al., SIAM J. Appl. Dyn. Syst. 22, No. 1, 199--234 (2023; Zbl 07674591) Full Text: DOI
Cui, Na; Zhang, Tingcong Inertial manifolds for the 3D hyperviscous Navier-Stokes equation with \(L^2\) force. (English) Zbl 07812733 Math. Methods Appl. Sci. 45, No. 17, 10543-10561 (2022). MSC: 35B40 35B42 35Q30 76F20 PDFBibTeX XMLCite \textit{N. Cui} and \textit{T. Zhang}, Math. Methods Appl. Sci. 45, No. 17, 10543--10561 (2022; Zbl 07812733) Full Text: DOI
Venditti, Claudia; Adrover, Alessandra; Giona, Massimiliano On the dynamic role of energy in underdamped particle motion. (English) Zbl 07515907 Physica A 597, Article ID 127285, 4 p. (2022). MSC: 82-XX PDFBibTeX XMLCite \textit{C. Venditti} et al., Physica A 597, Article ID 127285, 4 p. (2022; Zbl 07515907) Full Text: DOI
Venditti, Claudia; Adrover, Alessandra; Giona, Massimiliano Inertial effects and long-term transport properties of particle motion in washboard potential. (English) Zbl 07482551 Physica A 585, Article ID 126407, 18 p. (2022). MSC: 82-XX PDFBibTeX XMLCite \textit{C. Venditti} et al., Physica A 585, Article ID 126407, 18 p. (2022; Zbl 07482551) Full Text: DOI