Evolution Equations, Semigroups and Functional Analysis

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This work explores a range of topics in mathematical analysis and control theory, focusing on infinite-dimensional optimal control problems and various types of equations. It delves into degenerate two-point problems and bounded solutions for quasi-linear parabolic problems featuring quadratic gradient terms. The study also addresses degenerate evolution systems that model the cardiac electric field at both micro- and macroscopic levels, as well as singular limits for nonlinear hyperbolic systems. Additionally, it examines bounded perturbations of Ornstein-Uhlenbeck semigroups and integrodifferential equations of Volterra type in Banach spaces. The text discusses quasi-linear equations in infinite-dimensional spaces and uniform attractors of nonautonomous dynamical systems with memory. Mathematical aspects of the ring cavity problem are analyzed, along with Hadamard well-posedness of weak solutions in nonlinear dynamic elasticity and von Karman systems. The work also covers applications of operator sums in studying singular behaviors in elliptic problems, identification issues related to thermal materials with memory loss, and generators of noncommuting semigroups. Furthermore, it addresses well-posedness for nonautonomous abstract Cauchy problems, the Cauchy problem for semilinear heat equations with singular initial data, and the asymptotic behavior of non-autonomous linear evolution equations. Finally, it touches on abs