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Volume 9, Issue 2
The Decoupling of Elastic Waves from a Weak Formulation Perspective

Junjiang Lai, Hongyu Liu, Jingni Xiao & Yifeng Xu

DOI: 10.4208/eajam.080818.121018

East Asian J. Appl. Math., 9 (2019), pp. 241-251.

Published online: 2019-03

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  • Abstract

Two weak formulations for the Lamé system with the boundary conditions of third and fourth types are proposed. It is shown that the regularity of the solutions and properties of the boundary surface guarantee the equivalence of variational and standard formulations of the problem. Moreover, if the boundary of $Ω$ is a Lipschitz polyhedron or if $\mathcal{S}$ ($x$) = 0 on $∂Ω$, the decoupling results of [8] are derived from the weak formulations.

  • Keywords

Lamé system, weak formulation, decoupling.

  • AMS Subject Headings

35J50, 74B05, 35J20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9- 241, author = {Junjiang Lai, Hongyu Liu, Jingni Xiao and Yifeng Xu}, title = {The Decoupling of Elastic Waves from a Weak Formulation Perspective}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {2}, pages = { 241--251}, abstract = {

Two weak formulations for the Lamé system with the boundary conditions of third and fourth types are proposed. It is shown that the regularity of the solutions and properties of the boundary surface guarantee the equivalence of variational and standard formulations of the problem. Moreover, if the boundary of $Ω$ is a Lipschitz polyhedron or if $\mathcal{S}$ ($x$) = 0 on $∂Ω$, the decoupling results of [8] are derived from the weak formulations.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.080818.121018 }, url = {http://global-sci.org/intro/article_detail/eajam/13080.html} }
TY - JOUR T1 - The Decoupling of Elastic Waves from a Weak Formulation Perspective AU - Junjiang Lai, Hongyu Liu, Jingni Xiao & Yifeng Xu JO - East Asian Journal on Applied Mathematics VL - 2 SP - 241 EP - 251 PY - 2019 DA - 2019/03 SN - 9 DO - http://doi.org/10.4208/eajam.080818.121018 UR - https://global-sci.org/intro/article_detail/eajam/13080.html KW - Lamé system, weak formulation, decoupling. AB -

Two weak formulations for the Lamé system with the boundary conditions of third and fourth types are proposed. It is shown that the regularity of the solutions and properties of the boundary surface guarantee the equivalence of variational and standard formulations of the problem. Moreover, if the boundary of $Ω$ is a Lipschitz polyhedron or if $\mathcal{S}$ ($x$) = 0 on $∂Ω$, the decoupling results of [8] are derived from the weak formulations.

Junjiang Lai, Hongyu Liu, Jingni Xiao and Yifeng Xu. (2019). The Decoupling of Elastic Waves from a Weak Formulation Perspective. East Asian Journal on Applied Mathematics. 9 (2). 241-251. doi:10.4208/eajam.080818.121018
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