Strichartz estimates for the wave equation on manifolds with boundary
Matthew D. Blair, Hart F. Smith, Christopher D. Sogge (2009)
Annales de l'I.H.P. Analyse non linéaire
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Strichartz estimates for the wave equation on manifolds with boundary
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We prove that the initial value problem for the semi-linear Schrödinger and wave equations is well-posed in the Besov space , when the nonlinearity is of type , for . This allows us to obtain self-similar solutions, as well as to recover previously known results for the solutions under weaker smallness assumptions on the data.
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Existence of Global Solutions to Supercritical Semilinear Wave Equations
Georgiev, V. (1996)
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∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology. In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was...