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This is the first of three papers on the geometry of KDV. It presents what purports to be a foliation of an extensive function space into which all known invariant manifolds of KDV fit naturally as special leaves. The two main themes are addition (each leaf has its private one) and unimodal spectral classes (each leaf has a spectral interpretation).

Global existence for the nonlinear equations of crystal optics

Otto Liess (1989)

Journées équations aux dérivées partielles

Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data

C. Bardos, P. Degond (1985)

Annales de l'I.H.P. Analyse non linéaire

Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions

Pierre Degond (1986)

Annales scientifiques de l'École Normale Supérieure

Global magnetofluidostatic fields (an unsolved PDE problem).

Lo Surdo, C. (1986)

International Journal of Mathematics and Mathematical Sciences

Global strong solutions of Vlasov's equation---necessary and sufficient conditions for their existence

E. Horst (1987)

Banach Center Publications

$H^{2}$ convergence of solutions of a biharmonic problem on a truncated convex sector near the angle $π$

Abdelkader Tami, Mounir Tlemcani (2021)

Applications of Mathematics

We consider a biharmonic problem $Δ^{2} u_{ω} = f_{ω}$ with Navier type boundary conditions $u_{ω} = Δ u_{ω} = 0$ , on a family of truncated sectors $Ω_{ω}$ in $ℝ^{2}$ of radius $r$ , $0 < r < 1$ and opening angle $ω$ , $ω \in (2 π / 3, π]$ when $ω$ is close to $π$ . The family of right-hand sides ${(f_{ω})}_{ω \in (2 π / 3, π]}$ is assumed to depend smoothly on $ω$ in $L^{2} (Ω_{ω})$ . The main result is that $u_{ω}$ converges to $u_{π}$ when $ω \to π$ with respect to the $H^{2}$ -norm. We can also show that the $H^{2}$ -topology is optimal for such a convergence result.

Hartree-Fock theory in nuclear physics

D. Gogny, P. L. Lions (1986)

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

Homogénéisation et compacité par compensation

L. Tartar (1978/1979)

Séminaire Équations aux dérivées partielles (Polytechnique)

How many are affine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2014)

Archivum Mathematicum

The question how many real analytic affine connections exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables.

How many are equiaffine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2015)

Archivum Mathematicum

The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables.

Il criterio dell'energia e Vequazione di Maxwell-Cattaneo nella termodinamica dei sistemi elettromagnetici non lineari

Ettore Laserra, Giovanni Matarazzo (1985)

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

We study the evolution law of the canonical energy of an electromagnetic material, immersed in an environment that is thermally and electromagnetically passive, at constant temperature. We use as constitutive equation for the heat flux a Maxwell-Cattaneo like equation.

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Formule de Trotter pour l’opérateur $- Δ + q^{+} - q^{-} + i q^{'}$

Generalized Weierstrass ...-functions and KP flows in affine spaces.

Generations of waves at an inertial surface due to explosions.

Geometrical interpretation of the sinh-Gordon equation

Geometrische Eigenschaften der Lösungen der Differentialgleichung (1-zz)2wzz - n(n + 1) w= 0.

Geometry of KDV (1): Addition and the unimodular spectral classes.