4,229 research outputs found
Minimality properties of set-valued processes and their pullback attractors
We discuss the existence of pullback attractors for multivalued dynamical
systems on metric spaces. Such attractors are shown to exist without any
assumptions in terms of continuity of the solution maps, based only on
minimality properties with respect to the notion of pullback attraction. When
invariance is required, a very weak closed graph condition on the solving
operators is assumed. The presentation is complemented with examples and
counterexamples to test the sharpness of the hypotheses involved, including a
reaction-diffusion equation, a discontinuous ordinary differential equation and
an irregular form of the heat equation.Comment: 33 pages. A few typos correcte
Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from −∞ and goes to ∞ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the complete model is proved to be also gradient-like. The interest of this extension comes, for instance, in models where a continuum of equilibrium points holds, and for example a Lojasiewicz-Simon condition is satisfied. Indeed, we illustrate the usefulness of the theory with several examples.Fundação de Amparo à Pesquisa do Estado de São PauloConselho Nacional de Desenvolvimento Científico e TecnológicoCoordenação de aperfeiçoamento de pessoal de nivel superiorMinisterio de Ciencia e InnovaciónJunta de AndalucíaMinisterio de Educació
Operator matrices as generators of cosine operator functions
We introduce an abstract setting that allows to discuss wave equations with
time-dependent boundary conditions by means of operator matrices. We show that
such problems are well-posed if and only if certain perturbations of the same
problems with homogeneous, time-independent boundary conditions are well-posed.
As applications we discuss two wave equations in and in
equipped with dynamical and acoustic-like boundary conditions,
respectively
Stability analysis of abstract systems of Timoshenko type
We consider an abstract system of Timoshenko type where the operator is strictly positive
selfadjoint. For any fixed , the stability properties of
the related solution semigroup are discussed. In particular, a general
technique is introduced in order to prove the lack of exponential decay of
when the spectrum of the leading operator is not made by eigenvalues
only.Comment: Corrected typo
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