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Shock formation in a multidimensional viscoelastic diffusive system

Publication ,  Journal Article
Cohen, DS; White, AB; Witelski, TP
Published in: SIAM Journal on Applied Mathematics
January 1, 1995
Published version (DOI)

We examine a model for non-Fickian 'sorption overshoot' behavior in diffusive polymer-penetrant systems. The equations of motion proposed by Cohen and White [SIAM J. Appl. Math., 51 (1991), pp. 472-483] are solved for two-dimensional problems using matched asymptotic expansions. The phenomenon of shock formation predicted by the model is examined and contrasted with similar behavior in classical reaction-diffusion systems. Mass uptake curves produced by the model are examined and shown to compare favorably with experimental observations.

Duke Scholars

Thomas P. Witelski
Author Thomas P. Witelski Mathematics

Published In

SIAM Journal on Applied Mathematics

DOI

10.1137/S0036139993269333

ISSN

0036-1399

Publication Date

January 1, 1995

Volume

55

Issue

2

Start / End Page

348 / 368

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Cohen, D. S., White, A. B., & Witelski, T. P. (1995). Shock formation in a multidimensional viscoelastic diffusive system. SIAM Journal on Applied Mathematics, 55(2), 348–368. https://doi.org/10.1137/S0036139993269333
Cohen, D. S., A. B. White, and T. P. Witelski. “Shock formation in a multidimensional viscoelastic diffusive system.” SIAM Journal on Applied Mathematics 55, no. 2 (January 1, 1995): 348–68. https://doi.org/10.1137/S0036139993269333.
Cohen DS, White AB, Witelski TP. Shock formation in a multidimensional viscoelastic diffusive system. SIAM Journal on Applied Mathematics. 1995 Jan 1;55(2):348–68.
Cohen, D. S., et al. “Shock formation in a multidimensional viscoelastic diffusive system.” SIAM Journal on Applied Mathematics, vol. 55, no. 2, Jan. 1995, pp. 348–68. Scopus, doi:10.1137/S0036139993269333.
Cohen DS, White AB, Witelski TP. Shock formation in a multidimensional viscoelastic diffusive system. SIAM Journal on Applied Mathematics. 1995 Jan 1;55(2):348–368.

Published In

SIAM Journal on Applied Mathematics

DOI

10.1137/S0036139993269333

ISSN

0036-1399

Publication Date

January 1, 1995

Volume

55

Issue

2

Start / End Page

348 / 368

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics