Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

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Focusing on the investigation of nonlinear elliptic problems, this book employs a dynamical system approach to explore symmetrization and stabilization properties of nonnegative solutions in asymptotically symmetric unbounded domains. It introduces innovative methods for analyzing infinite-dimensional systems and finite-dimensional reductions, utilizing trajectory dynamical systems and new Liouville-type results. Additionally, it highlights symmetry and monotonicity in solutions to characterize asymptotic profiles, offering valuable insights for mathematical biologists.