The Nonlinearly Damped Oscillator

Juan Luis Vázquez

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A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence

Cédric Galusinski (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system $i \partial_{t} E + \nabla (\nabla . E) - α^{2} \nabla \times \nabla \times E = - {| E |}^{2 σ} E,$ where $E : ℝ^{3} \to ℂ^{3}$ . This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The -subcritical (that is 2/3) and the -subcritical (that is 2) are studied. In the physical case = 1, the limit is then studied for the $H^{1} (ℝ^{3})$ norm.

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

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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  $\{- div (a (x) (1 + {| \nabla u |}^{2})^{\frac{p - 2}{2}} {\nabla u) + b (x) (1 + | \nabla u |}^{2})^{\frac{λ}{2}} = f in Ω, u = 0 on \partial Ω,$  where Ω is a bounded open subset of $ℝ^{N}$ , N > 2, 2-1/, belongs to (Ω), $a (x) \geq α_{0} > 0$ , is a function in (Ω), is a function in $L^{r} (Ω)$ and 0 ≤ λ < λ *(), for some and λ *().

An improved derandomized approximation algorithm for the max-controlled set problem

Carlos Martinhon, Fábio Protti (2011)

RAIRO - Theoretical Informatics and Applications

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A vertex of a graph = () is said to be by $M \subseteq V$ if the majority of the elements of the neighborhood of (including itself) belong to . The set is a in if every vertex $i \in V$ is controlled by . Given a set $M \subseteq V$ and two graphs = ( $V, E_{1}$ ) and = ( $V, E_{2}$ ) where $E_{1} \subseteq E_{2}$ , the consists of deciding whether there exists a sandwich graph = () (, a graph where $E_{1} \subseteq E \subseteq E_{2}$ ) such that is a monopoly in = (). If the answer to the is No, we then consider the , whose objective is to find a sandwich...

An improved derandomized approximation algorithm for the max-controlled set problem

Carlos Martinhon, Fábio Protti (2011)

RAIRO - Theoretical Informatics and Applications

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Lower semicontinuity of multiple µ-quasiconvex integrals

Ilaria Fragalà (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Lower semicontinuity results are obtained for multiple integrals of the kind $\int_{ℝ^{n}} f (x, \nabla_{μ} u) d μ$ , where is a given positive measure on $ℝ^{n}$ , and the vector-valued function belongs to the Sobolev space $H_{μ}^{1, p} (ℝ^{n}, ℝ^{m})$ associated with . The proofs are essentially based on blow-up techniques, and a significant role is played therein by the concepts of tangent space and of tangent measures to . More precisely, for fully general , a notion of quasiconvexity for along the tangent bundle to , turns out to be necessary for...