By Patricia Anderson, Stephen R. Bernfeld (auth.), K. Vajravelu (eds.)

ISBN-10: 0792368673

ISBN-13: 9780792368670

ISBN-10: 1461302773

ISBN-13: 9781461302773

ISBN-10: 1461379741

ISBN-13: 9781461379744

The foreign convention on Differential Equations and Nonlinear Mechanics used to be hosted via the collage of vital Florida in Orlando from March 17-19, 1999. one of many convention days was once devoted to Professor V. Lakshmikantham in th honor of his seventy five birthday. 50 good confirmed execs (in differential equations, nonlinear research, numerical research, and nonlinear mechanics) attended the convention from thirteen nations. Twelve of the attendees brought hour lengthy invited talks and last thirty-eight provided invited forty-five minute talks. In each one of those talks, the focal point was once at the fresh advancements in differential equations and nonlinear mechanics and their purposes. This booklet involves 29 papers in keeping with the invited lectures, and that i think that it offers a sensible choice of complex themes of present curiosity in differential equations and nonlinear mechanics. i'm indebted to the dept of arithmetic, university of Arts and Sciences, division of Mechanical, fabrics and Aerospace Engineering, and the place of work of foreign reviews (of the collage of critical Florida) for the monetary help of the convention. additionally, to the math division of the collage of primary Florida for offering secretarial and administrative counsel. i want to thank the contributors of the neighborhood organizing committee, Jeanne clean, Jackie Callahan, John Cannon, Holly Carley, Brad Pyle, Pete Rautenstrauch, and June Wingler for his or her advice. thank you also are end result of the convention organizing committee, F. H. Busse, J. R. Cannon, V. Girault, R. H. J. Grimshaw, P. N. Kaloni, V.

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87, 1982,7431-7444. [15] Choudhury, S. Roy, Kelvin-Helmholtz instabiJites of supersonic, magnetized shear layers, J. Plasma Phys. 35,1986,375-392. , On the Kelvin-Helmholtz instabilites of structured plasma magnetosphere, Planetary and Space Science 34, 1985, 1223-1227. layers in the [17) Fujimota, M. , Ion inertia effect on the Kelvin-Helmholtz instability, 1. Geophysical Res. 96, 1991, 15725-15734. C. , Magnetospheric plasma waves, Astrophys. Space Sci. 200, 1993,107-115. , Chaos in Kelvin-Helmholtz instability in magnetic fluids, Phys.

114, 1991,57-77. Y. , 34, 1998,617-628. Y. , Global existence of classical solutions for degenerate quasi linear parabolic problems with slow diffusions, preprint. Y. , Existence of classical solutions for degenerate semi linear parabolic problems, Appl. Math. , 101, 1999, 125-149. Y. , Blow-up at the boundary for degenerate quasi linear parabolic problems with slow diffusions, preprint. 4 SUPERASYMPTOTIC PERTURBATION ANALYSIS OF THE KELVIN-HELMHOLTZ INSTABILITY OF SUPERSONIC SHEAR LAYERS s. Roy Choudhury Department of Mathematics University of Central Florida Orlando, Florida 32816-1364 A global asymptotic analysis of the traveling wave Kelvin-Helmholtz instability of a supersonic, finite-width velocity shear layer is carried out.

3) has two turning points in the potential term at u = ±I, as well as the regular singular point at the layer where u = 0 for the neutrally stable case ~ = O. The regular singular point at u = 0 is the location of the wave-fluid resonance V ph = wrfkz = v z • Here, we shall consider traveling modes with wr = wrl > 0 (with the understanding that equivalent solutions with wr = -wrl and the same value of Wi exist) [14]. The wave-fluid resonance occurs at X = x. 9) From earlier numerical results [14,15], we know that Wr ~ A, and ~ ~ 0 in the short-wavelength regime B2 » 1.

### Differential Equations and Nonlinear Mechanics by Patricia Anderson, Stephen R. Bernfeld (auth.), K. Vajravelu (eds.)

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