On a nonlinear wave equation with a nonlocal boundary condition
Consider the initial-boundary value problem for the nonlinear wave equation utt − µ(t)uxx + K|u| p−2u + λ|ut| q−2ut = F(x, t), 0 < x < 1, 0 < t < T, µ(t)ux(0, t) = K0u(0, t) + Rt 0 k (t − s) u (0, s) ds + g(t), −µ(t)ux(1, t) = K1u(1, t) + λ1|ut(1, t)| α−2ut(1, t), u(x, 0) = ue0(x), ut(x,...
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| Định dạng: | Journal Article |
| Ngôn ngữ: | English |
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Spinger
2017
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| Truy cập trực tuyến: | http://journals.math.ac.vn/acta/images/stories/pdf1/Vol_36_No_2/Bai15_Ngoc_Thuyet_Son_Long_2010_63.pdf http://digital.lib.ueh.edu.vn/handle/UEH/56261 |
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oai:localhost:UEH-562612020-01-06T03:26:34Z On a nonlinear wave equation with a nonlocal boundary condition Le Thi Phuong Ngoc Tran Minh Thuyet Pham Thanh Son Nguyen Thanh Long Galerkin method A priori estimates Asymptotic expansion of the solution up to order N Consider the initial-boundary value problem for the nonlinear wave equation utt − µ(t)uxx + K|u| p−2u + λ|ut| q−2ut = F(x, t), 0 < x < 1, 0 < t < T, µ(t)ux(0, t) = K0u(0, t) + Rt 0 k (t − s) u (0, s) ds + g(t), −µ(t)ux(1, t) = K1u(1, t) + λ1|ut(1, t)| α−2ut(1, t), u(x, 0) = ue0(x), ut(x, 0) = ue1(x), where p, q, α ≥ 2; K0, K1, K ≥ 0; λ, λ1 > 0 are given constants and µ, F, g, k, ue0, ue1, are given functions. First, the existence and uniqueness of a weak solution are proved by using the Galerkin method. Next, with α = 2, we obtain an asymptotic expansion of the solution up to order N in two small parameters λ, λ1 with error p λ2 + λ 2 1 N+ 1 2 . 2017-11-03T10:13:47Z 2017-11-03T10:13:47Z 2011 Journal Article 0251-4184 (Print), 2315-4144 (Online) http://journals.math.ac.vn/acta/images/stories/pdf1/Vol_36_No_2/Bai15_Ngoc_Thuyet_Son_Long_2010_63.pdf http://digital.lib.ueh.edu.vn/handle/UEH/56261 en ACTA Mathematica Vietnamica Vol. 36, No.2 none Portable Document Format (PDF) 345 374 Spinger |
| institution |
Đại học Kinh tế Thành phố Hồ Chí Minh |
| collection |
DSpaceUEH |
| language |
English |
| topic |
Galerkin method A priori estimates Asymptotic expansion of the solution up to order N |
| spellingShingle |
Galerkin method A priori estimates Asymptotic expansion of the solution up to order N Le Thi Phuong Ngoc On a nonlinear wave equation with a nonlocal boundary condition |
| description |
Consider the initial-boundary value problem for the nonlinear wave equation utt − µ(t)uxx + K|u| p−2u + λ|ut| q−2ut = F(x, t), 0 < x < 1, 0 < t < T, µ(t)ux(0, t) = K0u(0, t) + Rt 0 k (t − s) u (0, s) ds + g(t), −µ(t)ux(1, t) = K1u(1, t) + λ1|ut(1, t)| α−2ut(1, t), u(x, 0) = ue0(x), ut(x, 0) = ue1(x), where p, q, α ≥ 2; K0, K1, K ≥ 0; λ, λ1 > 0 are given constants and µ, F, g, k, ue0, ue1, are given functions. First, the existence and uniqueness of a weak solution are proved by using the Galerkin method. Next, with α = 2, we obtain an asymptotic expansion of the solution up to order N in two small parameters λ, λ1 with error p λ2 + λ 2 1 N+ 1 2 . |
| author2 |
Tran Minh Thuyet |
| author_facet |
Tran Minh Thuyet Le Thi Phuong Ngoc |
| format |
Journal Article |
| author |
Le Thi Phuong Ngoc |
| author_sort |
Le Thi Phuong Ngoc |
| title |
On a nonlinear wave equation with a nonlocal boundary condition |
| title_short |
On a nonlinear wave equation with a nonlocal boundary condition |
| title_full |
On a nonlinear wave equation with a nonlocal boundary condition |
| title_fullStr |
On a nonlinear wave equation with a nonlocal boundary condition |
| title_full_unstemmed |
On a nonlinear wave equation with a nonlocal boundary condition |
| title_sort |
on a nonlinear wave equation with a nonlocal boundary condition |
| publisher |
Spinger |
| publishDate |
2017 |
| url |
http://journals.math.ac.vn/acta/images/stories/pdf1/Vol_36_No_2/Bai15_Ngoc_Thuyet_Son_Long_2010_63.pdf http://digital.lib.ueh.edu.vn/handle/UEH/56261 |
| work_keys_str_mv |
AT lethiphuongngoc onanonlinearwaveequationwithanonlocalboundarycondition |
| _version_ |
1810055152708616192 |