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Displaying similar documents to “Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in L 1 ( Ω )

A model collision operator for the drift Fokker-Planck equation for applications to transport problems in magnetoplasmas

Massimo Tessarotto (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Nella Nota viene presentato un modello di operatore di collisione per l’equazione cinetica di (deriva) di Fokker-Planck, valido per magnetoplasmi quiescenti immersi in configurazioni idromagnetiche di equilibrio simmetriche. Principale caratteristica del presente modello è di consentire - contrariamente ad operatori di collisione approssimati in precedenza proposti da altri autori - la determinazione di variabili macroscopiche rilevanti includendo correzioni del primo ordine in termini...

On the algebraic properties of the H n 2 , 1 2 spaces

Sergiu Klainerman, Matei Machedon (1997-1998)

Séminaire Équations aux dérivées partielles

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We investigate the multiplicative properties of the spaces H n 2 , 1 2 As in the case of the classical Sobolev spaces H n 2 this space does not form an algebra. We investigate instead the space H n 2 L , more precisely a subspace of it formed by products of solutions of the homogeneous wave equation with data in H n 2 .

A model collision operator for the drift Fokker-Planck equation for applications to transport problems in magnetoplasmas

Massimo Tessarotto (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Nella Nota viene presentato un modello di operatore di collisione per l’equazione cinetica di (deriva) di Fokker-Planck, valido per magnetoplasmi quiescenti immersi in configurazioni idromagnetiche di equilibrio simmetriche. Principale caratteristica del presente modello è di consentire - contrariamente ad operatori di collisione approssimati in precedenza proposti da altri autori - la determinazione di variabili macroscopiche rilevanti includendo correzioni del primo ordine in termini...

Existence of multiple solutions for some functional boundary value problems

Staněk, Svatoslav (1992)

Archivum Mathematicum

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Let X be the Banach space of C 0 -functions on 0 , 1 with the sup norm and α , β X R be continuous increasing functionals, α ( 0 ) = β ( 0 ) = 0 . This paper deals with the functional differential equation (1) x ' ' ' ( t ) = Q [ x , x ' , x ' ' ( t ) ] ( t ) , where Q : X 2 × R X is locally bounded continuous operator. Some theorems about the existence of two different solutions of (1) satisfying the functional boundary conditions α ( x ) = 0 = β ( x ' ) , x ' ' ( 1 ) - x ' ' ( 0 ) = 0 are given. The method of proof makes use of Schauder linearizatin technique and the Schauder fixed point theorem. The results are modified for 2nd...

On the L p -stabilization of the double integrator subject to input saturation

Yacine Chitour (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a finite-dimensional control system ( Σ ) x ˙ ( t ) = f ( x ( t ) , u ( t ) ) , such that there exists a feedback stabilizer k that renders x ˙ = f ( x , k ( x ) ) globally asymptotically stable. Moreover, for ( H , p , q ) with H an output map and 1 p q , we assume that there exists a 𝒦 -function α such that H ( x u ) q α ( u p ) , where x u is the maximal solution of ( Σ ) k x ˙ ( t ) = f ( x ( t ) , k ( x ( t ) ) + u ( t ) ) , corresponding to u and to the initial condition x ( 0 ) = 0 . Then, the gain function G ( H , p , q ) of ( H , p , q ) given by G ( H , p , q ) ( X ) = def sup u p = X H ( x u ) q , is well-defined. We call profile of k for ( H , p , q ) any 𝒦 -function which is of the same order of...

Asymmetric heteroclinic double layers

Michelle Schatzman (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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Let W be a non-negative function of class C 3 from 2 to , which vanishes exactly at two points 𝐚 and 𝐛 . Let S 1 ( 𝐚 , 𝐛 ) be the set of functions of a real variable which tend to 𝐚 at - and to 𝐛 at + and whose one dimensional energy E 1 ( v ) = W ( v ) + | v ' | 2 / 2 d x is finite. Assume that there exist two isolated minimizers z + and z - of the energy E 1 over S 1 ( 𝐚 , 𝐛 ) . Under a mild coercivity condition on the potential W and a generic spectral condition on the linearization of the one-dimensional Euler–Lagrange operator...

Relaxation of quasilinear elliptic systems via A-quasiconvex envelopes

Uldis Raitums (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the weak closure W Z of the set Z of all feasible pairs (solution, flow) of the family of potential elliptic systems where Ω 𝐑 n is a bounded Lipschitz domain, F s are strictly convex smooth functions with quadratic growth and S = { σ m e a s u r a b l e σ s ( x ) = 0 or 1 , s = 1 , , s 0 , σ 1 ( x ) + + σ s 0 ( x ) = 1 } . We show that W Z is the zero level set for an integral functional with the integrand Q being the 𝐀 -quasiconvex envelope for a certain function and the operator 𝐀 = ( curl,div ) m . If the functions F s are isotropic, then on the characteristic cone...

Bond ionization energies: thiophosphoryl compounds

Marco V. Andreocci, Carla Cauletti, Claudio Furlani (1977)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Negli spettri fotoelettronici (p.e.) indotti da radiazione ultra-violetta di serie omologhe di composti, si trovano bande in ben definite regioni di energia, che possono essere assegnate empiricamente a ionizzazione di legami specifici o di coppie solitarie di elettroni. L’effetto dell'intorno chimico sulle energie di ionizzazione si esplica in piccoli spostamenti, che hanno una dipendenza approssimativamente lineare dall'ettronegatività di atomi o gruppi vicini. La discussione riguarda...