Results 21 to 30 of about 8,097 (311)
Journal of Optimization, Differential Equations and Their Applications, 2023 The paper investigates the issue of stability with respect to external disturbances for the global attractor of the wave equation under conditions that do not ensure the uniqueness of the solution to the initial problem.
Oleksiy V. Kapustyan +3 more
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Examples of global attractors in parabolic problems [PDF]
Hokkaido Mathematical Journal, 1998 The authors consider parabolic systems of the form: \[ u_t=-Au+f(x,u,D^1u, \dots, D^{2m-1} u),\;B_ju=0 \quad\text{for} \quad t>0,\;x\in\Omega, \tag{1} \] \[ j=1, \dots, md \quad \text{and} \quad u(0,x)= u_0(x),\;x\in \partial \Omega, \] with \(\Omega\) a smooth bounded domain, \(u=(u_1, \dots, u_d)\) and \(A\) an elliptic matrix operator of order \(2m\)
CARVALHO, Alexandre N. +2 more
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On the regularity of global attractors
Discrete & Continuous Dynamical Systems - A, 2009 This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract result, the semigroup generated by the strongly damped wave equation $$u_{tt}- u_t- u+ (u)=f$$ with critical ...
CONTI, MONICA, PATA, VITTORINO
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A Geometric Approach to the Global Attractor Conjecture [PDF]
SIAM Journal on Applied Dynamical Systems, 2014 v2: 49 pages, 8 figures, minor changes; v1: 48 pages, 8 ...
Ezra Miller +2 more
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Asymptotic Dynamics of a New Mechanochemical Model in Biological Patterns
Mathematical Modelling and Analysis, 2017 In this paper, we prove the existence of attractor for a new mechanochemical model with Neumann boundary conditions on a bounded domain of space dimension n ≤ 3.
Aibo Liu, Changchun Liu
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Global Attractor for Second-Order Nonlinear Evolution Differential Inclusions
Complexity, 2021 In this paper, we address the model of global attractor formulated in the form of evolution differential inclusions with second order in Banach spaces. Firstly, based on the fixed point theorem, the existence result of mild solutions is deduced. Then, by
Guangwang Su, Funing Lin
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Global Attractors of Evolutionary Systems [PDF]
Journal of Dynamics and Differential Equations, 2009 An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system $\mathcal{E}$ with respect to weak and strong topologies was introduced in [8] primarily to study the long-time behavior of the 3D Navier-Stokes equations (NSE) for which the existence of a semigroup of solution operators is not known.
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AIMS Mathematics, 2023 Our aim in this paper is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory involving two temperatures and a nonlinear coupling. In particular, we prove well-posedness results. More precisely, the existence and
Grace Noveli Belvy Louvila +3 more
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Strong Global Attractors for 3D Wave Equations with Weakly Damping
Abstract and Applied Analysis, 2012 We consider the existence of the global attractor A1 for the 3D weakly damped wave equation. We prove that A1 is compact in (H2(Ω)∩H01(Ω))×H01(Ω) and attracts all bounded subsets of (H2(Ω)∩H01(Ω))×H01(Ω) with respect to the norm of (H2(Ω)∩H01(Ω))×H01(Ω).
Fengjuan Meng
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AIMS Mathematics, 2020 In this article, we are interested in the study of Parabolic system of Cahn-Hilliard with a proliferation term and Dirichet boundary conditions. In particular, we prove the existence and the uniqueness of the solution, the existence of the global ...
Aymard Christbert Nimi, Daniel Moukoko
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