The observability of Burgers' equation, the Riccati equation, and the heat equation

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The observability of Burgers' equation, the Riccati equation, and the heat equation

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dc.creator El-Qasas, Majed Omar en_US
dc.date.available 2011-02-18T23:19:42Z en_US
dc.date.issued 1995-05 en_US
dc.identifier.uri http://hdl.handle.net/2346/19804 en_US
dc.description.abstract The 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. en_US
dc.language.iso en_US en_US
dc.publisher Texas Tech University en_US
dc.subject Heat equation en_US
dc.subject Burgers equation en_US
dc.subject Riccati equation en_US
dc.title The observability of Burgers' equation, the Riccati equation, and the heat equation en_US
dc.type Electronic Dissertation en_US
dc.degree.department Mathematics en_US
dc.degree.discipline Mathematics en_US
dc.degree.grantor Texas Tech University en_US
dc.degree.level Doctoral en_US
dc.degree.name Ph.D. en_US
dc.rights.availability unrestricted en_US

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