http://worldcat.org/entity/work/id/137315810

Research on Nonlinear Differential Equations

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).

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