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Existence of permanent and breaking waves for a shallow water equation : a geometric approach

Adrian Constantin (2000)

Annales de l'institut Fourier

The existence of global solutions and the phenomenon of blow-up of a solution in finite time for a recently derived shallow water equation are studied. We prove that the only way a classical solution could blow-up is as a breaking wave for which we determine the exact blow-up rate and, in some cases, the blow-up set. Using the correspondence between the shallow water equation and the geodesic flow on the manifold of diffeomorphisms of the line endowed with a weak Riemannian structure, we give sufficient...

Fonctions composées différentiables : cas algébrique

Jean-Claude Tougeron (1980)

Annales de l'institut Fourier

Soit f un morphisme propre et de Nash d’un ouvert Ω de R n dans un ouvert Ω ' de R p . Nous démontrons que l’image par f * de l’algèbre C ∞ ( Ω ' ) des fonctions réelles C ∞ dans Ω ' est fermée dans C ∞ ( Ω ) munie de sa topologie habituelle d’espace de Fréchet. Ce résultat généralise, dans le cas algébrique, un résultat de G. Glaeser sur les fonctions composées différentiables.

Function spaces of Nikolskii type on compact manifold

Cristiana Bondioli (1992)

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

Nikolskii spaces were defined by way of translations on R n and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in R n , we get an equivalent definition if we replace translations by all isometries of R n . This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for homogeneous...

Functional equations in real-analytic functions

G. Belitskii, V. Tkachenko (2000)

Studia Mathematica

The equation φ (x) = g(x,φ (x)) in spaces of real-analytic functions is considered. Connections between local and global aspects of its solvability are discussed.

Generating varieties for the triple loop space of classical Lie groups

Yasuhiko Kamiyama (2003)

Fundamenta Mathematicae

For G = SU(n), Sp(n) or Spin(n), let C G ( S U ( 2 ) ) be the centralizer of a certain SU(2) in G. We have a natural map J : G / C G ( S U ( 2 ) ) → Ω ₀ ³ G . For a generator α of H ⁎ ( G / C G ( S U ( 2 ) ) ; ℤ / 2 ) , we describe J⁎(α). In particular, it is proved that J ⁎ : H ⁎ ( G / C G ( S U ( 2 ) ) ; ℤ / 2 ) → H ⁎ ( Ω ₀ ³ G ; ℤ / 2 ) is injective.

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