Blow up of solutions for Klein-Gordon equations in the Reissner-Nordstrom metric
| dc.contributor.author | Georgiev, Svetlin G. | |
| dc.date.accessioned | 2021-05-28T14:31:05Z | |
| dc.date.available | 2021-05-28T14:31:05Z | |
| dc.date.issued | 2005-06-27 | |
| dc.description.abstract | In 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→0 | |
| dc.description.abstract | u | |
| dc.description.abstract | Ḃγ p,p (ℝ+) = ∞. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Georgiev, 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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13654 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Partial differential equation | |
| dc.subject | Klein-Gordon | |
| dc.subject | Blow up | |
| dc.title | Blow up of solutions for Klein-Gordon equations in the Reissner-Nordstrom metric | |
| dc.type | Article |