Blow-up of solutions to a nonlinear wave equation
| dc.contributor.author | Georgiev, Svetlin G. | |
| dc.date.accessioned | 2021-04-26T14:45:23Z | |
| dc.date.available | 2021-04-26T14:45:23Z | |
| dc.date.issued | 2004-05-26 | |
| dc.description.abstract | We study the solutions to the radial 2-dimensional wave equation Xtt - 1/ r Xr - Xrr + sinh2X/ 2r2 = g, X(1, r) = X∘ ∈ Ḣγ rad, Xt(1, r) = X1 ∈ Ḣγ-1rad, where r = |x| and x in ℝ2. We show that this Cauchy problem, with values into a hyperbolic space, is ill posed in subcritical Sobolev spaces. In particular, we construct a function g(t, r) in the space Lp ([0, 1]Lqrad), with 1/p + 2/q = 3 - γ, 0 < γ < 1, p ≥ 1, and 1 < q ≤ 2, for which the solution satisfies limt→0 ∥x̄∥Ḣγ rad = ∞. In doing so, we provide a counterexample to estimates in [1]. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 7 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Georgiev, S. G. (2004). Blow-up of solutions to a nonlinear wave equation. <i>Electronic Journal of Differential Equations, 2004</i>(77), pp. 1-7. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13431 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, 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, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Wave equation | |
| dc.subject | Blow-up | |
| dc.subject | Hyperbolic space | |
| dc.title | Blow-up of solutions to a nonlinear wave equation | en_US |
| dc.type | Article |