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

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

The foreign convention on Differential Equations and Nonlinear Mechanics used to be hosted via the collage of valuable 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 proven pros (in differential equations, nonlinear research, numerical research, and nonlinear mechanics) attended the convention from thirteen international locations. Twelve of the attendees introduced hour lengthy invited talks and closing thirty-eight awarded invited forty-five minute talks. In each one of those talks, the focal point used to be at the fresh advancements in differential equations and nonlinear mechanics and their functions. This publication involves 29 papers according to the invited lectures, and that i think that it presents a good choice of complex issues of present curiosity in differential equations and nonlinear mechanics. i'm indebted to the dep. of arithmetic, university of Arts and Sciences, division of Mechanical, fabrics and Aerospace Engineering, and the workplace of foreign reviews (of the college of relevant Florida) for the monetary help of the convention. additionally, to the maths division of the collage of crucial Florida for delivering secretarial and administrative information. i need 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 counsel. thank you also are a result of convention organizing committee, F. H. Busse, J. R. Cannon, V. Girault, R. H. J. Grimshaw, P. N. Kaloni, V.

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Fluids 28, 1985,3292-3301. , Hydromagnetic oscillations of a tangential discontinuity in the CGL approximation, Phys. Fluids 13, 1970,1503-1509. , Radiation of hydromagnetic waves from a tangential velocity discontinuity, Phys. Fluids 14, 1971,2067-2071. 48 Choudhury [231 Duhau, S. , Effect of compressibility on the stability of a vortex sheet in an ideal magnetofluid, Phys. Fluids 16, 1972, 150-152. , Discontinuities and the magnetosphere phenomena, J. Atm. Terr. Phys. 40, 1978,991-1000. , Discontinuities in the magnetosphere, Astrophys.

V f)2 n) an 2 f f3(ai1 1 ) n+f3xVfafl ds. f(V i1f·V f)+! xz} nds. 14) 54 2. 1) with Hamiltonian density ex = ±[t +(V f)2 - ~2 (V ft + ~ (l1f)2 + ~ (V 1,)2]. 1). The latter is of higher order in f3, but it cannot be neglected without destroying the Galilean invariance. 42) from [13]). The appropriate boundary conditions yield the balance of wave momentum. 3. ONE-DIMENSIONAL VERSION For two-dimensional flows the velocity potential and the surface elevation do not depend on the coordinate y. Naturally it is ID for the surface variables.

In press. [301 Brown, K. and Choudhury, S. Roy, Quasiperiodicity and Chaos in the Nonlinear Evolution of the Kelvin-Helmholtz Instability of Supersonic Anisotropic Tangential Velocity Discontinutities, J. Nonlin. , submitted. , Handbook of Applied Mathematics. Van Nostrand Reinhold, New York, 1983, 667. , Asymptotic Expansions: Their Derivation and Interpretation, Academic, London, 1973. V. , Hyperasymptotics, Proc. Roy. Soc. London A430, 1990,657-667. , Asymptotics, Superasymptotics, Hyperasymptotics, in Asymptotics Beyond All Orders, H.

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