Browsing by Author "Carvalho, Alexandre Nolasco"
Now showing items 1-19 of 19
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Article
A gradient-like non autonomous evolution process
(2009)In this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u ...
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Article
A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
(2011)In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), ...
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Article
An Estimate On the Fractal Dimension of Attractors of Gradient-Like Dynamical Systems
(2012)This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like ...
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Presentation
Atractores en dominios tipo dumbbell
(2007-09)En este trabajo, analizamos el comportamiento de la dinámica asintótica de una ecuación de reacción-difusión con condiciones ...
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Article
Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system
(Elsevier, 2007-05-15)In this paper we determine the exact structure of the pullback attractors in non-autonomous problems that are perturbations ...
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Article
Continuity of Lyapunov Functions and of Energy Level for a Generalized Gradient Semigroup
(2012)The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there ...
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Article
Equi-attraction and continuity of attractors for skew-product semiflows
(American Institute of Mathematical Sciences, 2016-11)In this paper we prove the equivalence between equi-attraction and continuity of attractors for skew-product semi-flows, ...
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Article
Existence of Pullback Attractors for Pullback Asymptotically Compact Processes
(2010)This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results ...
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Article
Finite-dimensional global attractors in Banach spaces
(Elsevier, 2010-12-15)We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is ...
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PhD Thesis
Finite-dimensionality of attractors for dynamicl systems wigh applications: deterministic and random settings
(2021-01-27)In this work we obtain estimates on the fractal dimension of attractors in three different settings: global attractors ...
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Article
Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
(Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies, 2013-12)We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system ...
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Article
Non-autonomous morse-decomposition and Lyapunov functions for gradient-like processes
(2013)We define (time dependent) Morse-decompositions for non-autonomous evolution processes (non-autonomous dynamical systems) ...
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Article
Robustness of dynamically gradient multivalued dynamical systems
(American Institute of Mathematical Sciences, 2019-03)In this paper we study the robustness of dynamically gradient multivalued semiflows. As an application, we describe the ...
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PhD Thesis
Robustness of nonuniform and random exponential dichotomies with applications to differential equations
(2022-03-17)In this thesis, we study hyperbolicity for deterministic and random nonautonomous dynamical systems and their applications ...
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Article
Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results
(Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies, 2015-06)In this work we study several questions concerning to abstract fractional Cauchy problems of order α ∈ (0, 1). Concretely, ...
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Article
Skew Product Semiflows and Morse Decomposition
(2013)This paper is devoted to the investigation of the dynamics of non-autonomous differential equations. The description of ...
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Article
Stability of Gradient Semigroups Under Perturbations
(2011)In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) ...
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Article
The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations
(ScienceDirect, 2021-01-01)In this work, we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic ...
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Chapter of Book
The sub-supersolution method for Kirchhoff systems: applications
(Springer, 2015)In this paper we prove that the sub-supersolution method works for general Kirchhoff systems. We apply the cited method to prove the existence of positive solutions for some specific models.