Displaying similar documents to “Resonance in Preisach systems”

Motion with friction of a heavy particle on a manifold. Applications to optimization

Alexandre Cabot (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Let Φ : H be a 𝒞 2 function on a real Hilbert space and Σ H × the manifold defined by Σ : = Graph ( Φ ) . We study the motion of a material point with unit mass, subjected to stay on Σ and which moves under the action of the gravity force (characterized by g > 0 ), the reaction force and the friction force ( γ > 0 is the friction parameter). For any initial conditions at time t = 0 , we prove the existence of a trajectory x ( . ) defined on + . We are then interested in the asymptotic behaviour of the trajectories when t + . More...

Classification of positive solutions of p -Laplace equation with a growth term

Matteo Franca (2004)

Archivum Mathematicum

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We give a structure result for the positive radial solutions of the following equation: Δ p u + K ( r ) u | u | q - 1 = 0 with some monotonicity assumptions on the positive function K ( r ) . Here r = | x | , x n ; we consider the case when n > p > 1 , and q > p * = n ( p - 1 ) n - p . We continue the discussion started by Kawano et al. in [KYY], refining the estimates on the asymptotic behavior of Ground States with slow decay and we state the existence of S.G.S., giving also for them estimates on the asymptotic behavior, both as r 0 and as r . We make use of a Emden-Fowler...

The Landau-Lifshitz equations and the damping parameter

K. Hamdache, M. Tilioua (2006)

Bollettino dell'Unione Matematica Italiana

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The present paper is particularly devoted to the damping effect in ferromagnetic materials. We are interested in determining the sensitivity of the LLG method solution to the phenomenological damping parameter a. We discuss the behaviour of the global weak solutions with finite energy of the Landau-Lifshitz equations when the damping parameter a tends either to 0 (underdamped case) or + (overdamped case).

Gradient theory for plasticity via homogenization of discrete dislocations

Adriana Garroni, Giovanni Leoni, Marcello Ponsiglione (2010)

Journal of the European Mathematical Society

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We deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal under study, so that the mathematical formulation will involve a two-dimensional variational problem. The dislocations are introduced as point topological defects of the strain fields, for which we compute the elastic energy stored outside the so-called core region. We show that the Γ -limit of this energy (suitably...

Further ultimate boundedness of solutions of some system of third order nonlinear ordinary differential equations

A. U. Afuwape, Mathew Omonigho Omeike (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper, we shall give sufficient conditions for the ultimate boundedness of solutions for some system of third order non-linear ordinary differential equations of the form X w i d t h 0 p t h e i g h t 5 . 46 p t t o 8 p t . . . + F ( X ¨ ) + G ( X ˙ ) + H ( X ) = P ( t , X , X ˙ , X ¨ ) where X , F ( X ¨ ) , G ( X ˙ ) , H ( X ) , P ( t , X , X ˙ , X ¨ ) are real n -vectors with F , G , H : n n and P : × n × n × n n continuous in their respective arguments. We do not necessarily require that F ( X ¨ ) , G ( X ˙ ) and H ( X ) are differentiable. Using the basic tools of a complete Lyapunov Function, earlier results are generalized.

Essential norms of the Neumann operator of the arithmetical mean

Josef Král, Dagmar Medková (2001)

Mathematica Bohemica

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Let K m ( m 2 ) be a compact set; assume that each ball centered on the boundary B of K meets K in a set of positive Lebesgue measure. Let C 0 ( 1 ) be the class of all continuously differentiable real-valued functions with compact support in m and denote by σ m the area of the unit sphere in m . With each ϕ C 0 ( 1 ) we associate the function W K ϕ ( z ) = 1 σ m m K g r a d ϕ ( x ) · z - x | z - x | m x of the variable z K (which is continuous in K and harmonic in K B ). W K ϕ depends only on the restriction ϕ | B of ϕ to the boundary B of K . This gives rise to a linear operator W K ...

Asymptotic behavior of solutions of a 2 n t h order nonlinear differential equation

C. S. Lin (2002)

Czechoslovak Mathematical Journal

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In this paper we prove two results. The first is an extension of the result of G. D. Jones [4]: (A) Every nontrivial solution for ( - 1 ) n u ( 2 n ) + f ( t , u ) = 0 , in ( α , ) , u ( i ) ( ξ ) = 0 , i = 0 , 1 , , n - 1 , and ξ ( α , ) , must be unbounded, provided f ( t , z ) z 0 , in E × and for every bounded subset I , f ( t , z ) is bounded in E × I . (B) Every bounded solution for ( - 1 ) n u ( 2 n ) + f ( t , u ) = 0 , in , must be constant, provided f ( t , z ) z 0 in × and for every bounded subset I , f ( t , z ) is bounded in × I .