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Solutions with Singular Initial Data for a Model of Electrophoretic Separation

Published online by Cambridge University Press:  20 November 2018

Joel D. Avrin
Joel D. Avrin*
Affiliation:
University of North Carolina at Charlotte, Charlotte, North Carolina 28223
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Abstract

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Unique global strong solutions of a Cauchy problem arising in electrophoretic separation are constructed with arbitrary initial data in L1, thus generalizing an earlier global existence result. For small diffusion coefficients, the solutions can be viewed as approximate solutions for the corresponding zero-diffusion Riemann problem.

Keywords

35K35B
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 3 - 10
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Adams, R. A., Sobolev Spaces, Academic Press, New York, 1975.Google Scholar
2. Avrin, J., The generalized Benjamin-Bona-Mahony equation in Rn with singular initial data, Nonlinear Analysis 11 (1987), 139–147.Google Scholar
3. Avrin, J., The generalized Burger's equation and the Navier-Stokes equation in Rn with singular initial data, Proc. A.M.S. 101 (1987), 29–40.Google Scholar
4. Avrin, J., Global existence for a model of electrophoretic separation, SIAM J. Math. Analysis, 19 (1988), 520–527.Google Scholar
5. Deyl, Z., éd., Electrophoresis: A Survey of Techniques and Applications, Elsevier, Amsterdam, 1979.Google Scholar
6. Fife, P. C., Palusinski, O. A., and Su, V., Electrophoretic traveling waves, Trans. Am. Math. Soc, to appear.Google Scholar
7. Friedman, A., Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969.Google Scholar
8. Geng, X., in preparation.Google Scholar
9. Giga, Y., Weak and strong solutions of the Navier-Stokes initial-value problem, Publ. RIMS, Kyoto Univ. 19(1983), 887–910.Google Scholar
10. Hoff, D., and Smoller, J., Solutions in the large for certain nonlinear parabolic systems, Ann. Inst. Henri Poincaré 2 (1985), 213–235.Google Scholar
11. Reed, M., Abstract Non-Linear Wave Equations, Springer-Verlag, Berlin, Heidelberg, and New York, 1975.Google Scholar
12. Saville, D. A., and Palusinski, O. A., Theory of electrophoretic separation, Part 1 and Part 2, AICHE Journal 32 (1986), no. 2.Google Scholar
13. Weissler, F. B., Local existence and non-existence for semilinear parabolic equations in Lp , Ind. Univ. Math. Jnl. 29 (1980), 79–102.Google Scholar
14. Weissler, F. B., The Navier-Stokes initial value problem in Lp , Arch. Rat. Mech. Analysis 74 (1980), '219-230.Google Scholar