Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

Conceptual Idea of Identification of Patterns and Problem Solving in the Human’s Memory and the Possibilities to Use it in Artificial Intelligent

Given cybernetic idea is formed on the basis of neurophysiologic, neuropsychological, neurocybernetic data and verisimilar hypotheses, which fill gaps of formers, of the author as well. First of all attention is focused on general principles of a Memory organization in the brain and processes which take part in it that realize such psychical functions as perception and identification of input information about patterns and a problem solving, which is specified by the input and output conditions, as well. Realization of the second function, essentially cogitative, is discussed in the aspects of figurative and lingual thinking on the levels of intuition and understanding. The reasons of advisability and principles of bionic approach to creation of appropriate tools of artificial intelligent are proposed.

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.

Principles of Extremum and Application to some Problems of Analysis

AMS subject classification: 41A17, 41A50, 49Kxx, 90C25.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

Extended Maximum Principles

2000 Mathematics Subject Classification: 35B50, 35L15.