Browsing by Author "Abu Qarnayn, Naif"

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Optimal Control Problems with Linear and Non-linear Damped Viscous Wave Equations
(THE UNIVERSITY OF TEXAS AT ARLINGTON, 2025-05) Abu Qarnayn, Naif; Souvik, Roy
In this thesis, we focus on the analysis and numerical solution of nonsmooth optimal control problems governed by a class of linear and nonlinear Damped viscous wave equations with both linear and nonlinear source mechanisms. These equations play a crucial role in modeling wave propagation in complex media, with significant applications in medical imaging and therapeutic interventions. Using advanced numerical techniques, we explore the complex interplay between damping, viscosity, and control strategies to enhance precision in control problems related to wave-like equations. The work provides valuable frameworks into optimizing wave dynamics, leading to improved methodologies in fields such as photoacoustic imaging, lithotripsy, and tissue elastography.
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