- 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.
- R. Brahadwaj, B. Mohammadi and J. Santiago, Design and optimization of on-chip capillary electrophoresis. Electrophoresis J. 23 (2002) 2729–2744. [CrossRef]
- G. Bruin, Recent developments in electrokinetically driven analysis of microfabricated devices. Electrophoresis 21 (2000) 3931–3951. [CrossRef] [PubMed]
- A. Douglis and L. Nirenberg, Interior estimates for elliptic systems of partial differential equations. Comm. Pure Appl. Math. 8 (1955) 503–538. [CrossRef] [MathSciNet]
- 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.
- S.D. Eidelman, Parabolic equations, in Partial differential equations VI, M.A. Shubin Ed., Encyclopaedia of Mathematical Sciences 63, Springer (1994) 201–313.
- M.G. El Hak, The MEMS Handbook, Handbook series for Mechanical Engineering 7. CRC Press (2002).
- K. Krupchyk, W. Seiler and J. Tuomela, Overdetermined elliptic systems. Found. Comp. Math. 6 (2006) 309–351. [CrossRef]
- K. Krupchyk and J. Tuomela, Completion of overdetermined parabolic PDEs. J. Symb. Comput. 43 (2008) 153–167. [CrossRef]
- 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.
- M. Marden, On the zeros of certain rational functions. Trans. Amer. Math. Soc. 32 (1930) 658–668. [CrossRef] [MathSciNet]
- B. Mohammadi and J. Tuomela, Simplifying numerical solution of constrained PDE systems through involutive completion. ESAIM: M2AN 39 (2005) 909–929. [CrossRef] [EDP Sciences]
- B. Mohammadi and J. Tuomela, Involutive upgrades of Navier-Stokes solvers. Int. J. Comput. Fluid Dyn. 23 (2009) 439–447. [CrossRef] [MathSciNet]
- M. Oddy and J. Santiago, Multiple-species model for electrokinetic instability. Phys. Fluids 17 (2005) 1245–1278.
- B. Perthame, Transport equations in biology, Frontiers in Mathematics. Birkhäuser, Basel (2007).
- T. Poinsot and D. Veynante, Theoretical and Numerical Combustion. 2nd edn., R.T. Edwards, Inc. (2005).
- J.F. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups. Mathematics and its applications 14. Gordon and Breach Science Publishers (1978).
- R.F. Probstein, Physicochemical Hydrodynamics. Wiley (1995).
- W. Seiler, Involution – The Formal Theory of Differential Equations and its Applications in Computer Algebra. Algorithms and Computation in Mathematics 24. Springer, 2010.
- 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]
- D. Spencer, Overdetermined systems of linear partial differential equations. Bull. Amer. Math. Soc. 75 (1969) 179–239. [CrossRef] [MathSciNet]
- T. Squires and S.R. Quake, Instability of electrokinetic microchannel flows with conductivity gradients. Rev. Mod. Phys. 77 (2005) 977–1026. [CrossRef]
Volume 45, Number 5, September-October 2011
|Page(s)||901 - 913|
|Published online||15 April 2011|