A nonlinear wave equation with a nonlinear integral equation involving the boundary value
| dc.contributor.author | Nguyen, Thanh Long | |
| dc.contributor.author | Bui, Tien Dung | |
| dc.date.accessioned | 2021-04-26T20:50:17Z | |
| dc.date.available | 2021-04-26T20:50:17Z | |
| dc.date.issued | 2004-09-03 | |
| dc.description.abstract | We consider the initial-boundary value problem for the nonlinear wave equation utt - uxx + ƒ(u, ut) = 0, x ∈ Ω = (0, 1), 0 < t < T, ux(0, t) = P(t), u(1, t) = 0, u(x, 0) = u0(x), ut(x, 0) = u1(x), where u0, u1, ƒ are given functions, the unknown function u(x, t) and the un-known boundary value P(t) satisfy the nonlinear integral equation P(t) = g(t) + H(u(0, t)) - ∫t0 K(t - s, u(0, s))ds, where g, K, H are given functions. We prove the existence and uniqueness of weak solutions to this problem, and discuss the stability of the solution with respect to the functions g, H and K. For the proof, we use the Galerkin method. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Nguyen, T. L., & Bui, T. D. (2004). A nonlinear wave equation with a nonlinear integral equation involving the boundary value. <i>Electronic Journal of Differential Equations, 2004</i>(103), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13457 | |
| 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, 2004, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Galerkin method | |
| dc.subject | Integrodifferential equations | |
| dc.subject | Schauder fixed point theorem | |
| dc.subject | Weak solutions | |
| dc.subject | Stability of the solutions | |
| dc.title | A nonlinear wave equation with a nonlinear integral equation involving the boundary value | |
| dc.type | Article |