The critical case for a semilinear weakly hyperbolic equation
Date
2004-08-24
Authors
Fanelli, Luca
Lucente, Sandra
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We prove a global existence result for the Cauchy problem, in the three-dimensional space, associated with the equation u>tt - αλ (t)Δxu = -u|u|p(λ)-1 where αλ(t) ≥ 0 and behaves at (t - t0)λ close to some t0 > 0 with α(t0) = 0, and p(λ) = (3λ + 10) / (3λ + 2) with 3 ≤ p(λ) ≤ 5. This means that we deal with the superconformal, critical nonlinear case. Moreover we assume a small initial energy.
Description
Keywords
Global existence, Semilinear wave equations
Citation
Fanelli, L., & Lucente, S. (2004). The critical case for a semilinear weakly hyperbolic equation. <i>Electronic Journal of Differential Equations, 2004</i>(101), pp. 1-13.
Rights
Attribution 4.0 International