Exponential attractors for semilinear wave equations with damping
Albert Milani (1992)
Banach Center Publications
Similarity:
Albert Milani (1992)
Banach Center Publications
Similarity:
Jan W. Cholewa, Radoslaw Czaja, Gianluca Mola (2008)
Bollettino dell'Unione Matematica Italiana
Similarity:
Bi-space global and exponential attractors for the time continuous dynamical systems are considered and the bounds on their fractal dimension are discussed in the context of the smoothing properties of the system between appropriately chosen function spaces. The case when the system exhibits merely some partial smoothing properties is also considered and applications to the sample problems are given.
Alain Miranville (2003)
Applications of Mathematics
Similarity:
In this article we introduce the notion of a minimal attractor for families of operators that do not necessarily form semigroups. We then obtain some results on the existence of the minimal attractor. We also consider the nonautonomous case. As an application, we obtain the existence of the minimal attractor for models of Cahn-Hilliard equations in deformable elastic continua.
Zhonghuai Wu, Jianying Shao, Mingquan Yang, Wei Gao (2011)
Annales Polonici Mathematici
Similarity:
We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].
Fan, Xiaoming (2008)
Journal of Applied Mathematics
Similarity:
Ahmad Makki (2016)
Applications of Mathematics
Similarity:
We consider the viscous Allen-Cahn and Cahn-Hilliard models with an additional term called the nonlinear Willmore regularization. First, we are interested in the well-posedness of these two models. Furthermore, we prove that both models possess a global attractor. In addition, as far as the viscous Allen-Cahn equation is concerned, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. Finally, we give...
Houssem Eddine Khochemane, Sara Labidi, Sami Loucif, Abdelhak Djebabla (2025)
Mathematica Bohemica
Similarity:
We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping...
Ravi P. Agarwal, Alexander Domoshnitsky, Abraham Maghakyan (2015)
Czechoslovak Mathematical Journal
Similarity:
We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones....
Lluís Alsedà, Sara Costa (2009)
Fundamenta Mathematicae
Similarity:
The aim of this paper is twofold. On the one hand, we want to discuss some methodological issues related to the notion of strange nonchaotic attractor. On the other hand, we want to formulate a precise definition of this kind of attractor, which is "observable" in the physical sense and, in the two-dimensional setting, includes the well known models proposed by Grebogi et al. and by Keller, and a wide range of other examples proposed in the literature. Furthermore, we analytically prove...
Alexander Rezounenko (2014)
Open Mathematics
Similarity:
Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.