Souvik, RoyAbu Qarnayn, Naif2025-05-282025-05https://hdl.handle.net/20.500.14154/75475In 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.138enoptimal control theorynonlinear damped viscous wave equationfinite difference methednonlinear conjugate gradientoptimal controldamped viscous wave equationThesis