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Solution of multilayer diffusion problems via the Laplace transform

Journal Article


Abstract


  • We consider a one-dimensional multilayer diffusion problem subject to nonhomogeneous boundary conditions. Unlike previous results that used a separation of variables technique to solve such problems with homogeneous boundary conditions, here we use a Laplace transform approach. We reformulate the multilayer diffusion problem as a sequence of one-layer diffusion problems with arbitrary time-dependent functions, solve a general one-layer diffusion problem using the Laplace transform, and then use the interface conditions to determine a system of renewal-type equations for the time-dependent functions. Finally, these renewal equations are solved explicitly using the Laplace transform.

Publication Date


  • 2016

Citation


  • Rodrigo, M. R. & Worthy, A. L. (2016). Solution of multilayer diffusion problems via the Laplace transform. Journal of Mathematical Analysis and Applications, 444 (1), 475-502.

Scopus Eid


  • 2-s2.0-84993274195

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6188

Number Of Pages


  • 27

Start Page


  • 475

End Page


  • 502

Volume


  • 444

Issue


  • 1

Abstract


  • We consider a one-dimensional multilayer diffusion problem subject to nonhomogeneous boundary conditions. Unlike previous results that used a separation of variables technique to solve such problems with homogeneous boundary conditions, here we use a Laplace transform approach. We reformulate the multilayer diffusion problem as a sequence of one-layer diffusion problems with arbitrary time-dependent functions, solve a general one-layer diffusion problem using the Laplace transform, and then use the interface conditions to determine a system of renewal-type equations for the time-dependent functions. Finally, these renewal equations are solved explicitly using the Laplace transform.

Publication Date


  • 2016

Citation


  • Rodrigo, M. R. & Worthy, A. L. (2016). Solution of multilayer diffusion problems via the Laplace transform. Journal of Mathematical Analysis and Applications, 444 (1), 475-502.

Scopus Eid


  • 2-s2.0-84993274195

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6188

Number Of Pages


  • 27

Start Page


  • 475

End Page


  • 502

Volume


  • 444

Issue


  • 1