The critical case for a semilinear weakly hyperbolic equation
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We prove a global existence result for the Cauchy problem, in the three-dimensional space, associated with the equation
utt - 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.
CitationFanelli, L., & Lucente, S. (2004). The critical case for a semilinear weakly hyperbolic equation. Electronic Journal of Differential Equations, 2004(101), pp. 1-13.
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