Accession Number : AD0715738

Title :   Research on Nonlinear Differential Equations.

Descriptive Note : Final rept. 1 Sep 67-31 Aug 70,

Corporate Author : GEORGE WASHINGTON UNIV WASHINGTON D C

Personal Author(s) : Taam,C. T.

Report Date : 1970

Pagination or Media Count : 9

Abstract : The report presents a summary of research which was concerned with completing a detailed treatment of a nonlinear diffusion equation where the elliptic differential operator on the right side generates a stable holomorphic semi-group. The results obtained include the existence of three different types of unique global true solution u(t,x) which describes: a stable bounded orbit, a stable periodic orbit, and a stable almost periodic orbit. And the operator differential equations of the form du(t)/dt = Au(t), u(0) = x, in abstract spaces as dynamical systems. One has considered a solution as the orbit of a point x under the action of a semi-group of operators. The results obtained apply to various types of differential equations and Markov processes, including some partial differential equations and diffusion equations, and to classical non-conservative dynamical systems through their induced semi-groups of operators in appropriate function spaces. Also this research can be considered as a preliminary investigation of the dynamical behavior of semi-groups of nonlinear operators. (Author)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, OPERATORS(MATHEMATICS)), PARTIAL DIFFERENTIAL EQUATIONS, HILBERT SPACE, BANACH SPACE, TOPOLOGY, CONVERGENCE, FOURIER ANALYSIS, SERIES(MATHEMATICS), GROUPS(MATHEMATICS), STATISTICAL PROCESSES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE