
Accession Number : AD0715738
Title : Research on Nonlinear Differential Equations.
Descriptive Note : Final rept. 1 Sep 6731 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 semigroup. 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 semigroup 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 nonconservative dynamical systems through their induced semigroups of operators in appropriate function spaces. Also this research can be considered as a preliminary investigation of the dynamical behavior of semigroups 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