A Method Of Generalized Characteristics
Download A Method Of Generalized Characteristics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Method Of Generalized Characteristics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
A Method of Generalized Characteristics
Author: Marc A. Berger
language: en
Publisher: American Mathematical Soc.
Release Date: 1982
The classical and Brownian methods of characteristics are generalized to analyze evolution equations of arbitrary order. Calculi of higher orders, analogous to first order classical calculus and second order Ito calculus, are constructed. Solutions of differential equations in the calculi become characteristic propagators of higher order partial differential equations. The solutions of these partial differential equations are then represented as averages of random samples of initial data based on these characteristic flows, in a general sense.
Generalized Characteristics of First Order PDEs
Author: Arik Melikyan
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
In some domains of mechanics, physics and control theory boundary value problems arise for nonlinear first order PDEs. A well-known classical result states a sufficiency condition for local existence and uniqueness of twice differentiable solution. This result is based on the method of characteristics (MC). Very often, and as a rule in control theory, the continuous nonsmooth (non-differentiable) functions have to be treated as a solutions to the PDE. At the points of smoothness such solutions satisfy the equation in classical sense. But if a function satisfies this condition only, with no requirements at the points of nonsmoothness, the PDE may have nonunique solutions. The uniqueness takes place if an appropriate matching principle for smooth solution branches defined in neighboring domains is applied or, in other words, the notion of generalized solution is considered. In each field an appropriate matching principle are used. In Optimal Control and Differential Games this principle is the optimality of the cost function. In physics and mechanics certain laws must be fulfilled for correct matching. A purely mathematical approach also can be used, when the generalized solution is introduced to obtain the existence and uniqueness of the solution, without being aimed to describe (to model) some particular physical phenomenon. Some formulations of the generalized solution may meet the modelling of a given phenomenon, the others may not.
Generalization of Turbojet-engine Performance in Terms of Pumping Characteristics
Characteristics of a basic turbojet engine consisting of compressor, combustor, and turbine can be presented in terms of pumping characteristics; that is, corrected air flow, ratio of engine-outlet to -inlet total pressure, ratio of engine-outlet to -inlet total temperature, Reynolds number index, corrected engine speed, and corrected fuel-air ratio. Such a presentation describes the engine independently of the characteristics of other elements of the propulsion system. This method of presentation also permits rapid estimation of performance of complex propulsion systems involving the basic tubojet engine.