Semilinear wave equation on manifolds
نویسندگان
چکیده
منابع مشابه
The Semilinear Wave Equation on Asymptotically Euclidean Manifolds
We consider the quadratically semilinear wave equation on (R, g), d ≥ 3. The metric g is non-trapping and approaches the Euclidean metric like 〈x〉. Using Mourre estimates and the Kato theory of smoothness, we obtain, for ρ > 0, a Keel–Smith–Sogge type inequality for the linear equation. Thanks to this estimate, we prove long time existence for the nonlinear problem with small initial data for ρ...
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In this paper we shall show that certain estimates for the Euclidean wave equation also hold on Riemannian manifolds with smooth, strictly geodesically concave boundaries. By the last condition, we understand that the second fundamental form on the boundary of the manifold is strictly positive definite. We shall then give two applications of our estimates. First, we shall show that if n is the ...
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In this paper we shall show that certain estimates for the Euclidean wave equation also hold on Riemannian manifolds with smooth, strictly geodesically concave boundaries. By the last condition, we understand that the second fundamental form on the boundary of the manifold is strictly positive definite. We shall then give two applications of our estimates. First, we shall show that if n is the ...
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We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metric...
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2002
ISSN: 0240-2963
DOI: 10.5802/afst.1014