Existence and asymptotic expansion of solutions to a nonlinear wave equation with a memory condition at the boundary
| dc.contributor.author | Nguyen, Thanh Long | |
| dc.contributor.author | Truong, Le Xuan | |
| dc.date.accessioned | 2021-08-05T16:21:03Z | |
| dc.date.available | 2021-08-05T16:21:03Z | |
| dc.date.issued | 2007-03-20 | |
| dc.description.abstract | We study the initial-boundary value problem for the nonlinear wave equation utt - ∂/∂x (μ(x, t)ux) + K|u|p-2 u + λ|ut|q-2 ut = ƒ(x, t), u(0, t) = 0 -μ(1, t)ux (1, t) = Q(t), u(x, 0) = u0(x), ut(x, 0) = u1(x), where p ≥ 2, q ≥ 2, K, λ are given constants and u0, u1, ƒ, μ are given functions. The unknown function u(x, t) and the unknown boundary value Q(t) satisfy the linear integral equation. Q(t) = K1(t)u(1, t) + λ1(t)ut (1, t) - g(t) - ∫t0 k(t - s)u(1, s)ds, where K1, λ1, g, k are given functions satisfying some properties stated in the next section. This paper consists of two main sections. First, we prove the existence and uniqueness for the solutions in a suitable function space. Then, for the case K1(t) = K1 ≥ 0, we find the asymptotic expansion in K, λ, K1 of the solutions, up to order N + 1. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 19 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Long, N. T., & Truong, L. X. (2007). Existence and asymptotic expansion of solutions to a nonlinear wave equation with a memory condition at the boundary. <i>Electronic Journal of Differential Equations, 2007</i>(48), pp. 1-19. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14209 | |
| 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, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Nonlinear wave equation | |
| dc.subject | Linear integral equation | |
| dc.subject | Existence and uniqueness | |
| dc.subject | Asymptotic expansion | |
| dc.title | Existence and asymptotic expansion of solutions to a nonlinear wave equation with a memory condition at the boundary | |
| dc.type | Article |