We study local well-posedness of the Cauchy problem for two geometric wave equations that can be derived from Anti-Self-Dual Yang Mills equations on R2+2. These are the space-time Monopole Equation and the Ward Wave Map. The equations can be formulated in different ways. For the formulations we use, we establish local well-posedness results, which are sharp using the iteration methods. / text

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This work extends modelling of high prequency electric-acoustic transducers beyong current limiting approxilations, which is of interest to such applications as ultrasonic imaging, testing, tomography etc. / Thesis (PhD)--University of South Australia, 2001.

This work extends modelling of high frequency electric-acoustic transducers beyond current limiting approximations, which is of interest to such applications as ultrasonic imaging, testing, tomography etc. The developed methodology includes transient modelling of the acoustic potential field with dynamic Green?s functions and linear formulation of wave propagation in the moving reference frame. A finite difference model is determined to achieve fast numerical implementation. Developed is also experimental methodology for impulse response measurements, offering modifications of the inverse Wiener filter and introducing novel transducer equalisation increasing signal bandwidth. / thesis (PhD)--University of South Australia, 2001.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains x, 97 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 84-88).

Thesis (Ph. D.)--University of California, San Diego, 1997. / Vita. Includes bibliographical references.

It is intended that this paper present an acceptable proof of the existence of a solution for the wave equation.

Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.

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