Finite dimensional aspects of semilinear parabolic equations

1996 ◽  
Vol 8 (2) ◽  
pp. 177-202 ◽  
Author(s):  
Herbert Koch
Keyword(s):  
Parabolic Equations ◽  
Semilinear Parabolic Equations ◽  
Finite Dimensional ◽  
Semilinear Parabolic

Oscillations-Induced Transitions and Their Application in Control of Dynamical Systems

1990 ◽  
Vol 112 (3) ◽  
pp. 313-319 ◽  
Author(s):  
J. Bentsman
Keyword(s):  
Dynamical Systems ◽  
Parabolic Equations ◽  
Closed Loop ◽  
Distributed Parameter ◽  
Control Laws ◽  
Loop Control ◽  
Finite Dimensional ◽  
Analytical Tools ◽  
Semilinear Parabolic ◽  
Qualitative Changes

Studies of the use of oscillations for control purposes continue to reveal new practically important properties unique to the oscillatory open and closed loop control laws. The goal of this paper is to enlarge the available set of analytical tools for such studies by introducing a method of analysis of the qualitative changes in the behavior of dynamical systems caused by the zero mean parametric excitations. After summarizing and slightly refining a technique developed previously for the finite dimensional nonlinear systems, we consider an extension of this technique to a class of distributed parameter systems (DPS) governed by semilinear parabolic equations. The technique presented is illustrated by several examples.

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