Titlebook: Geometrical Optics and Related Topics; Ferruccio Colombini,Nicolas Lerner Conference proceedings 1997 Springer Science+Business Media New

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姑姑在炫耀

Dhoni Bushi,Oyi Dai Nimasow,Gibji Nimasowts a unique solution . to (1) satisfying .and .. Observe that this latter property means exactly that the nonlinear term . in (1) belongs to ., which allows us to consider it as a source term in the energy method. In particular, this implies . with conservation of energy ..

monopoly

显赫的人

Concentration effects in critical nonlinear wave equation and scattering theory,osedness of equation (1) in the energy space was proved rather recently by Shatah-Struwe [16]. Let us recall precisely this result: given . there exists a unique solution . to (1) satisfying .and .. Observe that this latter property means exactly that the nonlinear term . in (1) belongs to ., which

前面

Corral

,Sobolev embeddings in Weyl-Hörmander calculus,d to subelliptic systems of order two, see [4]. In this text, we focus on .. embeddings for abstract Sobolev spaces in the context of the Weyl-Hörmander calculus. The structure of this text will be the following: in the first section, we briefly present Weyl-Hörmander calculus, then we state the abs

河流

Global existence of the solutions and formation of singularities for a class of hyperbolic systems,ic systems of the form . with smooth compactly supported initial data in ... Here . ≥ 1 and .: .. → . is a given .. function. We shall call (0.1) a hyperbolic system of Hamiltonian type (see [5]). For the sake of simplicity, we shall concentrate our attention to the special case . with ., . > 1.

Debark

决定性

Nonlinear wave diffraction, space-time, called rays. Two examples of ray theories are the geometrical optics theory of light and semi-classical quantum mechanics. When applicable, ray theory is extremely powerful and it often provide surprisingly accurate quantitative results.

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