Georgiev, Svetlin G.2021-05-282021-05-282005-06-27Georgiev, S. G. (2005). Blow up of solutions for Klein-Gordon equations in the Reissner-Nordstrom metric. <i>Electronic Journal of Differential Equations, 2005</i>(67), pp. 1-22.1072-6691https://hdl.handle.net/10877/13654In this paper, we study the solutions to the Cauchy problem (utt - Δu)gs + m2</sup>u = ƒ(u), t ∈ (0, 1], x ∈ ℝ3, u(1, x) = u0 ∈ Ḃγp,p (ℝ3), ut (1, x) = u1 ∈ Ḃγ-1p,p (ℝ3), where gs is the Reissner-Nordströ m metric; p > 1, γ ∈ (0, 1), m ≠ 0 are constants, ƒ ∈ C2 (ℝ1), ƒ(0) = 0, 2m2|u| ≤ ƒ(l) (u) ≤ 3m2|u|, l = 0, 1. More precisely we prove that the Cauchy problem has unique nontrivial solution in C((0, 1] Ḃγp,p (ℝ+)), u(t, r) = {v(t)ω(r) /0 for t ∈ (0, 1], r ≤ r1 for t ∈ (0, 1], r ≥ r1, where r = |x|, and limt→0uḂγ p,p (ℝ+) = ∞.Text22 pages1 file (.pdf)enAttribution 4.0 InternationalPartial differential equationKlein-GordonBlow upArticle