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dc.contributor.authorLong, Nguyen Thanh ( )
dc.identifier.citationLong, N. T. (2005). Nonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditions. Electronic Journal of Differential Equations, 2005(138), pp. 1-18.en_US

In this paper we consider the nonlinear wave equation problem

utt - B(∥u∥20, ∥ur20 (urr + 1/r ur) = ƒ(r, t, u, ur), 0 < r < 1, 0 < t < T,
| limr→0+ √rur(r, t)| < ∞,
ur(1, t) + hu(1, t) = 0,
u(r, 0) = ũ0(r), ut(r, 0) = ũ1(r).

To this problem, we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved, in weighted Sobolev using standard compactness arguments. In the latter part, we give sufficient conditions for quadratic convergence to the solution of the original problem, for an autonomous right-hand side independent on ur and a coefficient function B of the form B = B(∥u∥20) = b0 + ∥u∥20 with b0 > 0.

dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectNonlinear wave equationen_US
dc.subjectGalerkin methoden_US
dc.subjectQuadratic convergenceen_US
dc.subjectWeighted Sobolev spacesen_US
dc.titleNonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditionsen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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