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Title: Existence of Global Solutions to Supercritical Semilinear Wave Equations
Authors: Georgiev, V.
Keywords: Semilinear Wave Equation
Strichartz Estimate
Issue Date: 1996
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 22, No 2, (1996), 125p-164p
Abstract: 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 F. John in [13], where he established that for 1 < λ < 1+√2 the solution of (1.1) blows-up in finite time, while for λ > 1 + √2 the solution exists globally in time. Therefore, the value λ0 = 1 + √2 is critical for the semilinear wave equation (1.1).
Description: ∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.
ISSN: 1310-6600
Appears in Collections:Volume 22 Number 2

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