# Existence of Global Solutions to Supercritical Semilinear Wave Equations

Serdica Mathematical Journal (1996)

- Volume: 22, Issue: 2, page 125-164
- ISSN: 1310-6600

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topGeorgiev, 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 -

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