Existence of Global Solutions to Supercritical Semilinear Wave Equations

Georgiev, V.. "Existence of Global Solutions to Supercritical Semilinear Wave Equations." Serdica Mathematical Journal 22.2 (1996): 125-164. <http://eudml.org/doc/11636>.

@article{Georgiev1996,
abstract = {∗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 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).},
author = {Georgiev, V.},
journal = {Serdica Mathematical Journal},
keywords = {Semilinear Wave Equation; Strichartz Estimate; -estimates},
language = {eng},
number = {2},
pages = {125-164},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Existence of Global Solutions to Supercritical Semilinear Wave Equations},
url = {http://eudml.org/doc/11636},
volume = {22},
year = {1996},
}

TY - JOUR
AU - Georgiev, V.
TI - Existence of Global Solutions to Supercritical Semilinear Wave Equations
JO - Serdica Mathematical Journal
PY - 1996
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 22
IS - 2
SP - 125
EP - 164
AB - ∗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 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).
LA - eng
KW - Semilinear Wave Equation; Strichartz Estimate; -estimates
UR - http://eudml.org/doc/11636
ER -