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At least 271 records · Page 15

Dissipative systems

The abstract theory presented shows how the theory of dissipative systems of ordinary differential equations can be extended to include a wide class of functional and partial differential equations. Since the basic hypotheses are all in terms of boundedness, finding sufficient conditions in terms of Liapunov functions was not difficult. Work is being undertaken to solve some nontrivial examples to illustrate how the theory can applied.

Lasalle, J. P.↗

Dissipation of electric fields in the ionosphere

The heating and movement of the upper atmosphere at ionospheric levels in response to electric currents are discussed. Joule dissipation, generation of winds, and pressure gradients are significant factors in the energetics of the ionospheric electric currents flowing during magnetic storms and also of the Sq current system.

Cole, K. D.↗

Dissipative effects on nonlinear waves in rotating fluids.

Modifications to the existing inviscid theory of long-wave propagation in rotating fluids are studied. A modification to the Korteweg-deVries equation is found to describe weak dissipation in long waves in a swirling fluid. General features of solutions are discussed, and a solution for the damping of solitary waves is presented.

Leibovich, S.↗

Effects of viscosity and constraints on the dispersion and dissipation of waves in large blood vessels. I.

Investigation of the effects of blood viscosity on dissipation as well as dispersion of small waves in arteries and veins by means of a parametric study. A linearized analysis of axisymmetric waves in a cylindrical membrane that contains a viscous fluid indicates that there are two families of waves: a family of slow waves and one of fast waves. The faster waves are shown to be more sensitive to variations in the elastic properties of the medium surrounding the blood vessels and at high values of the frequency parameter alpha. At low values of alpha the effects of viscosity on attenuation are reversed.

Jones, E.↗

Dissipative systems.

A theory is presented that shows how the concept of dissipative systems of ordinary differential equations can be extended to include a broad class of functional and partial differential equations, such as retarded functional differential equations and parabolic partial differential equations. Since the basic hypotheses are all in terms of boundedness, finding sufficient conditions in terms of Liapunov functions would not be too difficult.

Lasalle, J. P.↗