THERMAL SCIENCE
International Scientific Journal
ASYMPTOTIC STABILITY OF ORBITAL ATTRACTORS FOR A CLASS OF NON-AUTONOMOUS THERMAL EQUATIONS
ABSTRACT
This paper examines the existence and asymptotic stability of orbital attractors for a class of non-autonomous thermal equations. The study employs the attractor theory in non-autonomous infinite-dimensional dynamical systems, in con-junction with the energy method, compression function method, and Kuratowski non-compactness measure theory. Verification of the existence of the orbital absorption set allows us to conclude that the orbital attractor exists when the non-linear term is independent of time and dependent on time.
KEYWORDS
PAPER SUBMITTED: 2023-08-04
PAPER REVISED: 2024-06-01
PAPER ACCEPTED: 2024-06-01
PUBLISHED ONLINE: 2025-07-06
THERMAL SCIENCE YEAR
2025, VOLUME
29, ISSUE
Issue 3, PAGES [1793 - 1802]
- Kashif, M., et al., A Novel Numerical Manner for Non-Linear Coupled Variable Order Reaction- Diffusion Eqaution, Thermal Science, 27 (2023), Spec. Issue 1, pp. S353-S363
- Chepyzhov, V. V., et al., A Minimal Approach to the Theory of Global Attractors, Discrete and Continuous Dynamical Systems, 32 (2012), 6, pp. 2079-2088
- Higazy, M., Aggarwal, S., Sawi Transformation for System of Ordinary Differential Equations with Application, Ain Shams Eng. J., 12 (2021), 3, pp. 3173-3182
- Caraballo, T., et al., Weak Pullback Attractors of Setvalued Processes, Journal of Mathematical Analysis and Applications, 282 (2003), 2, pp. 692-707
- Khan, F. S., Khalid, M., Fareeha Transform: A New Generalized Laplace Transform, Math. Meth. Appl Sci., 46 (2023), 9, pp. 11043-11057
- Tao, H., et al., The Aboodh Transformation-Based Homotopy Perturbation Method: New Hope for Fractional Calculus, Frontiers in Physics, 11 (2023), 1168795
- Deng, S.-X., et al.: Approximate Analytical Solution for Modified Korteweg-de Vries Equation With Local Fractional Derivative Via New Iterative Method, Thermal Science, 24 (2020), 6B, pp. 4027-4032
- Bradshaw, Z., Tsai, T.-P., On the Local Pressure Expansion for the Navier-Stokes Equations, J. Math. Fluid Mech. 24 (2022), 3, 32
- Cai, M., Li, C. P., Numerical Approaches to Fractional Integrals and Derivatives: A Review, Mathematics, 8 (2020), 1, 43
- Deng, S., et al., Approximate Analytical Solutions of Generalized Fractional Korteweg-de Vries Equation, Thermal Science, 27 (2023), 3A, pp. 1873-1879
- Deng, S., et al., Some Notes on the Maximum Principle of Semi-Linear Dynamical System, Thermal Science, 27 (2023), 3A, pp.1889-1897
- Perumal, S., et al., Heat Transfer Analysis in Counter Flow Shell and Tube Heat Exchanger Using De-sign of Experiments, Thermal Science, 26 (2022), 2A, pp. 843-848
- He, J.-H., et al., Non-Linear Instability of Two Streaming-Superposed Magnetic Reiner-Rivlin Fluids by He-Laplace Method, Journal of Electroanalytical Chemistry, 895 (2021), 115388
- Yang, X. J., The Zero-Mass Renormalization Group Differential Equations and Limit Cycles in Non-Smooth Initial Value Problems, Japan Agri. Res. Quart., 3 (2012), 9, pp. 229-235
- Kilbas, A., et al., Theory and Application of Fractional Differential Equation, Elsevier Science B.V., Amsterdam, The Netherlands, 2006