Free access
Issue
ESAIM: M2AN
Volume 45, Number 5, September-October 2011
Page(s) 901 - 913
DOI http://dx.doi.org/10.1051/m2an/2011001
Published online 15 April 2011
  1. M.S. Agranovich, Elliptic boundary problems, in Partial differential equations IX, M.S. Agranovich, Y.V. Egorov and M.A. Shubin Eds., Encyclopaedia of Mathematical Sciences 79, Springer (1997) 1–144.
  2. R. Brahadwaj, B. Mohammadi and J. Santiago, Design and optimization of on-chip capillary electrophoresis. Electrophoresis J. 23 (2002) 2729–2744. [CrossRef]
  3. G. Bruin, Recent developments in electrokinetically driven analysis of microfabricated devices. Electrophoresis 21 (2000) 3931–3951. [CrossRef] [PubMed]
  4. A. Douglis and L. Nirenberg, Interior estimates for elliptic systems of partial differential equations. Comm. Pure Appl. Math. 8 (1955) 503–538. [CrossRef] [MathSciNet]
  5. P. Dudnikov and S. Samborski, Linear overdetermined systems of partial differential equations, in Partial Differential Equations VIII, M. Shubin Ed., Encyclopaedia of Mathematical Sciences 65, Springer (1996) 1–86.
  6. S.D. Eidelman, Parabolic equations, in Partial differential equations VI, M.A. Shubin Ed., Encyclopaedia of Mathematical Sciences 63, Springer (1994) 201–313.
  7. M.G. El Hak, The MEMS Handbook, Handbook series for Mechanical Engineering 7. CRC Press (2002).
  8. K. Krupchyk, W. Seiler and J. Tuomela, Overdetermined elliptic systems. Found. Comp. Math. 6 (2006) 309–351. [CrossRef]
  9. K. Krupchyk and J. Tuomela, Completion of overdetermined parabolic PDEs. J. Symb. Comput. 43 (2008) 153–167. [CrossRef]
  10. H. Lin, B. Storey, M. Oddy, C.-H. Chen and J. Santiago, Instability of electrokinetic microchannel flows with conductivity gradients. Phys. Fluids 16 (2004) 1876–1899.
  11. M. Marden, On the zeros of certain rational functions. Trans. Amer. Math. Soc. 32 (1930) 658–668. [CrossRef] [MathSciNet]
  12. B. Mohammadi and J. Tuomela, Simplifying numerical solution of constrained PDE systems through involutive completion. ESAIM: M2AN 39 (2005) 909–929. [CrossRef] [EDP Sciences]
  13. B. Mohammadi and J. Tuomela, Involutive upgrades of Navier-Stokes solvers. Int. J. Comput. Fluid Dyn. 23 (2009) 439–447. [CrossRef] [MathSciNet]
  14. M. Oddy and J. Santiago, Multiple-species model for electrokinetic instability. Phys. Fluids 17 (2005) 1245–1278.
  15. B. Perthame, Transport equations in biology, Frontiers in Mathematics. Birkhäuser, Basel (2007).
  16. T. Poinsot and D. Veynante, Theoretical and Numerical Combustion. 2nd edn., R.T. Edwards, Inc. (2005).
  17. J.F. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups. Mathematics and its applications 14. Gordon and Breach Science Publishers (1978).
  18. R.F. Probstein, Physicochemical Hydrodynamics. Wiley (1995).
  19. W. Seiler, Involution – The Formal Theory of Differential Equations and its Applications in Computer Algebra. Algorithms and Computation in Mathematics 24. Springer, 2010.
  20. V.A. Solonnikov, On boundary value problems for linear parabolic systems of differential equations of general form. Trudy Mat. Inst. Steklov. 83 (1965) 3–163 (in Russian). [MathSciNet]
  21. D. Spencer, Overdetermined systems of linear partial differential equations. Bull. Amer. Math. Soc. 75 (1969) 179–239. [CrossRef] [MathSciNet]
  22. T. Squires and S.R. Quake, Instability of electrokinetic microchannel flows with conductivity gradients. Rev. Mod. Phys. 77 (2005) 977–1026. [CrossRef]

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