Stationary solutions of controlled generalized Burgers' equation



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Texas Tech University


Nonlinear evolution partial differential equations have been a frequent topic in recent research literature. One reason for this is that such equations describe nonlinear distributed parameter systems important in applications (e.g., fluid or gas flow). Of particular interest is the study of stationary solutions to these equations because knowledge of these solutions provides valuable information concerning the long time evolution of the system. Investigated in this work is the structure of the set of stationary solutions for a special class of boundary controlled nonlinear evolution equations. The method used is based on the application of a special nonlinear transformation which was introduced by F. Calogero and allows the linearization of the equations. The main result of this work is the existence of multiple stationary solutions for the problem. This result implies that the solutions of the system of equations may have a complicated "turbulent" behavior as time approaches infinity.