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Displaying similar documents to “Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems”

The Nonlinearly Damped Oscillator

Juan Luis Vázquez (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the large-time behaviour of the nonlinear oscillator m x ' ' + f ( x ' ) + k x = 0 , where and is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case   f ( x ' ) = A | x ' | α - 1 x '  with real, . We characterize the existence and behaviour of fast orbits, , orbits that stop in finite time.

Homogenization and localization in locally periodic transport

Grégoire Allaire, Guillaume Bal, Vincent Siess (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we study the homogenization and localization of a spectral transport equation posed in a locally periodic heterogeneous domain. This equation models the equilibrium of particles interacting with an underlying medium in the presence of a creation mechanism such as, for instance, neutrons in nuclear reactors. The physical coefficients of the domain are -periodic functions modulated by a macroscopic variable, where is a small parameter. The mean free path of the...

Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in  (Ω)

M. F. Betta, A. Mercaldo, F. Murat, M. M. Porzio (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we prove uniqueness results for the renormalized solution, if it exists, of a class of non coercive nonlinear problems whose prototype is
 - div ( a ( x ) ( 1 + | u | 2 ) p - 2 2 u ) + b ( x ) ( 1 + | u | 2 ) λ 2 = f in Ω , u = 0 on Ω , 
where Ω is a bounded open subset of N , N > 2, 2-1/, belongs to  (Ω), a ( x ) α 0 > 0 , is a function in (Ω), is a function in L r ( Ω ) and 0 ≤ λ < λ *(), for some and λ *().