Browsing by Subject "Burgers equation"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item Approximation methods for output regulation of nonlinear systems(Texas Tech University, 2003-12) Koskodan, Rachel C.The goal of this work is to develop an iterative method for obtaining approximate feedback laws for solving problems of geometric output regulation for a nonlinear system governed by Burgers' equation. We also present a method for solving the linearized output regulation problem which provides initial data for our iterative scheme. We provide an example which demonstrates the convergence of our iterative scheme to the exact value of the control found using a Hopf-Cole transformation.Item Stationary solutions of controlled generalized Burgers' equation(Texas Tech University, 1995-05) Dickens, Molly M.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.Item The observability of Burgers' equation, the Riccati equation, and the heat equation(Texas Tech University, 1995-05) El-Qasas, Majed OmarThe question of observability is that of recovering the initial data from a point measurement. This problem has been intensively studied by Martin, Gilliam. Wolf, etc. In this dissertation research we are looking at the observability of Burger's equation via the representation of solutions as ratio of solutions of the heat equation. This extends the work of Martin and Ghosh on the observability of Riccati equation. Also we have shown that the boundary data for the one-dimensional heat system given in Chapter II can be determined up to a linear equivalence relation in the Grassmannian manifold G'^{R^) by the spectra which can be recovered from a point observation. Finally, in Chapter III, we are looking at the explicit solution of the nonlinear Burgers' system.