Advanced Study in Behaviour of Solution of Nonlinear Random Differential Equations

Abstract

The nondeterministic nature of phenomena in the general areas of newlinebiological, engineering, oceanographic and Physical Sciences ,the mathematical newlinedescriptions of such phenomena frequently result in random equations. It is to newlinepresent theoretical results concerning certain classes of random equations and newlinethen to apply those results to problems that arise in the general areas. Usually, newlinethe mathematical models or the equations that have been used to describe a newlineparticular phenomenon or process of the universe contains a parameter, newlinewhich has some specific physically interpretations but whose values is not newlineknown. If any such phenomena involving mentioned parameters and which newlinesatisfy certain probabilistic and measure theoretic behavior with respect to newlinethis parameter, then we say it is a random phenomena. For example, in the newlinetheory of diffusion or heat conduction, we have the diffusion coefficient or newlinethe coefficient of conductivity that play the prominent role. Similarly in newlinethe case of wave theory, the propagation coefficient and in the theory of newlineelasticity, the modulus of elasticity play the significant role in the behavior newlineof the underlined processes. Thus, the coefficients or parameters that have newlinean important role to play in the natural and physical phenomena like above newlineare called random parameters. newlineAlso, the mathematical equations are solved using as the value of the newlineparameter or coefficients, the mean value of the set of observations newlineexperimentally obtained. However, if the experiment is performed repeatedly, newlinethen the mean values found will vary, and if the variation is large. The mean newlinevalue actually used may be quite unsatisfactory. Thus, in practice the physical newlineconstant is not really a constant, but a random variable whose behavior is newlinegoverned by some probability distribution. It is thus advantageous to view these newlineequations as being random rather than deterministic, to search random solution newlineand to study its statistical properties. We take about some parameters or newlineiii newlinecoefficients, the random analysis of the random