Separation of linear and nonlinear modes in a hyperbolic system describing electrophoresis
Author:
Heinrich Freistühler
Journal:
Quart. Appl. Math. 52 (1994), 31-34
MSC:
Primary 35L45; Secondary 35Q80, 76Z99, 92E99
DOI:
https://doi.org/10.1090/qam/1262315
MathSciNet review:
MR1262315
Full-text PDF Free Access
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Additional Information
L. Euler, Lettre de M. Euler à M. de la Grange, Recherches sur la propagation des ébranlements dans un milieu élastique, Misc. Taur. 2$^{2}$ (1760–1761) 1–10, 1762
J.-L. Lagrange, Application de la méthode exposée dans le mémoire précédent à la solution de différents problèmes de dynamique, Misc. Taur. 2$^{2}$ (1760–1761), 196–298, 1762
C. A. Truesdell, Rational fluid mechanics, 1687–1765 (= Editor’s introduction to) Leonhardi Euleri Commentationes ad Theoriam Fluidorum Pertinentes, Leonhardi Euleri Opera Omnia II, 12, Orell Féssl, Zurich, 1954
P. D. Lax, Hyperbolic Systems of Conservation Laws II, Commun. Pure Appl. Math. 10, 537–566 (1957)
O. A. Oleinik, Discontinuous solutions of nonlinear differential equations, Uspekhi Mat. Nauk 12, 3–73 (1957); English transl. in Amer. Math. Soc. Transl. Ser. 2 26, 95–172 (1963)
I. M. Gel’fand, Some problems in the theory of quasilinear equations, Uspekhi Mat. Nauk 14, 87–158 (1959); English transl. in Amer. Math. Soc. Transl. Ser. 2 29, 295–381 (1963)
H. Rhee, R. Aris, and N. R. Amundson, On the theory of multicomponent chromatography, Philos. Trans. Roy. Soc. London A 267, 419–455 (1970)
B. Temple, Systems of conservation laws with invariant submanifolds, Trans. Amer. Math. Soc. 280 (1983)
R. J. Leveque and B. Temple, Stability of Godunov’s scheme for a class of $2 \times 2$ systems of conservation laws, Trans. Amer. Math. Soc. 288, 115–123 (1985)
D. Serre, Solutions à variations bornées pour certains systèmes hyperboliques de lois de conservation, J. Differential Equations 68, 137–169 (1987)
D. Wagner, Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions, J. Differential Equations 68, 118–136 (1987)
D. Serre, Les ondes planes en électromagnétisme non linéaire, Physica D 31, 227–251 (1988)
X. Geng, The conservation laws in isotachophoresis model, Thesis, University of Arizona, 1990
C. Dafermos and X. Geng, Generalized characteristics, uniqueness, and regularity of solutions in a hyperbolic system of conservation laws, Ann. Inst. H. Poincaré Anal. Non Linéaire 8, 231–269 (1991)
D. Serre, Oscillations non linéaires des systèmes hyperboliques: Méthodes et résultats qualitatifs, Ann. Inst. H. Poincaré Anal. Non Linéaire 8, 351–417 (1991)
L. Euler, Lettre de M. Euler à M. de la Grange, Recherches sur la propagation des ébranlements dans un milieu élastique, Misc. Taur. 2$^{2}$ (1760–1761) 1–10, 1762
J.-L. Lagrange, Application de la méthode exposée dans le mémoire précédent à la solution de différents problèmes de dynamique, Misc. Taur. 2$^{2}$ (1760–1761), 196–298, 1762
C. A. Truesdell, Rational fluid mechanics, 1687–1765 (= Editor’s introduction to) Leonhardi Euleri Commentationes ad Theoriam Fluidorum Pertinentes, Leonhardi Euleri Opera Omnia II, 12, Orell Féssl, Zurich, 1954
P. D. Lax, Hyperbolic Systems of Conservation Laws II, Commun. Pure Appl. Math. 10, 537–566 (1957)
O. A. Oleinik, Discontinuous solutions of nonlinear differential equations, Uspekhi Mat. Nauk 12, 3–73 (1957); English transl. in Amer. Math. Soc. Transl. Ser. 2 26, 95–172 (1963)
I. M. Gel’fand, Some problems in the theory of quasilinear equations, Uspekhi Mat. Nauk 14, 87–158 (1959); English transl. in Amer. Math. Soc. Transl. Ser. 2 29, 295–381 (1963)
H. Rhee, R. Aris, and N. R. Amundson, On the theory of multicomponent chromatography, Philos. Trans. Roy. Soc. London A 267, 419–455 (1970)
B. Temple, Systems of conservation laws with invariant submanifolds, Trans. Amer. Math. Soc. 280 (1983)
R. J. Leveque and B. Temple, Stability of Godunov’s scheme for a class of $2 \times 2$ systems of conservation laws, Trans. Amer. Math. Soc. 288, 115–123 (1985)
D. Serre, Solutions à variations bornées pour certains systèmes hyperboliques de lois de conservation, J. Differential Equations 68, 137–169 (1987)
D. Wagner, Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions, J. Differential Equations 68, 118–136 (1987)
D. Serre, Les ondes planes en électromagnétisme non linéaire, Physica D 31, 227–251 (1988)
X. Geng, The conservation laws in isotachophoresis model, Thesis, University of Arizona, 1990
C. Dafermos and X. Geng, Generalized characteristics, uniqueness, and regularity of solutions in a hyperbolic system of conservation laws, Ann. Inst. H. Poincaré Anal. Non Linéaire 8, 231–269 (1991)
D. Serre, Oscillations non linéaires des systèmes hyperboliques: Méthodes et résultats qualitatifs, Ann. Inst. H. Poincaré Anal. Non Linéaire 8, 351–417 (1991)
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Article copyright:
© Copyright 1994
American Mathematical Society
