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Existence of Global Solutions to Supercritical Semilinear Wave Equations

Georgiev, V. — 1996

Serdica Mathematical Journal

∗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 studied by...

Does Atkinson-Wilcox Expansion Converges for any Convex Domain?

Arnaoudov, I.;  Georgiev, V.;  Venkov, G. — 2007

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40. The Atkinson-Wilcox theorem claims that any scattered field in the exterior of a sphere can be expanded into a uniformly and absolutely convergent series in inverse powers of the radial variable and that once the leading coefficient of the expansion is known the full series can be recovered uniquely through a recurrence relation. The leading coefficient of the series is known as the scattering amplitude...

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