The relation of the boundary conditions for the nonlinear singularly perturbed equation εy″+yy′-x ny=0,x∈(0,1),n≠-1,y(0)=α,y(1)=β and its shock solutions are discussed. Using the matching condition, the shock solutions and its existence conditions for nonlinear equations are obtained.
This model which is composed of constraint conditions from 6 non-linear equations and 13 inequalities is suitable to process the data obtained by CLS-3600 series logging tools, also can be used to process the logs by Schlumberger tools.
(2)The relation between the amplitude of scotopie b-waves and light intensitycan be adequately expressed by the non-linear equation V/V_(max)=I~a/(I~a+K~a),whereV is the amplitude elicited by light intensity Ⅰ,V_(max) is the maximum amplitude,aand K are constants.
A nonlinear equation that is satisfied by the optimal exercise boundaries of the perpetual Bermudan option is found.
A nonlinear equation containing a highest derivative of third order is obtained in the vicinity of the caustic for the case of special media in which the limiting velocities of sound in the mixture at rest are close in value.
At small flow rates, the study of long-wavelength perturbations reduces to the solution of an approximate nonlinear equation that describes the change in the film thickness [1-3].
Nonlinear equation for amplitude of Tollmien-Schlichting waves in a boundary layer
An unsteady nonlinear equation, more accurate than those derived in previous studies, is obtained for the process of wave formation on the surface of a vertically flowine film.
It is known that, contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled non-linear equations, whose closed-form solution derivation is a real challenge.
Inverse problems for linear and non-linear equations of mathematical physics
In the paper we consider inverse problems for evolutionary linear and non-linear equations.
Non-linear equations for simple chemical reactions with physical interactions
The method of functional derivation applied to non-equilibrium Green's functions is used to find non-linear equations of motion forD.