Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: Ordinary and partial differential systems; Optimal control of deterministic and stochastic evolution equations;Control theory of Partial Differential Equations (PDE''s); Optimization methods in PDE''s with numerous applications to mechanics and physics; Inverse problems; Stability theory; Abstract optimization problems; Calculus of variations; Numerical treatment of solutions to differential equations and related optimization problems.

These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering.

This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002. Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT program.

Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: Ordinary and partial differential systems; Optimal control of deterministic and stochastic evolution equations;Control theory of Partial Differential Equations (PDE's); Optimization methods in PDE's with numerous applications to mechanics and physics; Inverse problems; Stability theory; Abstract optimization problems; Calculus of variations; Numerical treatment of solutions to differential equations and related optimization problems.

These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering.

This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002. Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT program.

This book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes. These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media, as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability distributions.

The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs. It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include a solid foundation in functional analysis and probability theory.

Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: Ordinary and partial differential systems; Optimal control of deterministic and stochastic evolution equations;Control theory of Partial Differential Equations (PDE''s); Optimization methods in PDE''s with numerous applications to mechanics and physics; Inverse problems; Stability theory; Abstract optimization problems; Calculus of variations; Numerical treatment of solutions to differential equations and related optimization problems.

These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering.

This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002. Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT program.

Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: Ordinary and partial differential systems; Optimal control of deterministic and stochastic evolution equations;Control theory of Partial Differential Equations (PDE's); Optimization methods in PDE's with numerous applications to mechanics and physics; Inverse problems; Stability theory; Abstract optimization problems; Calculus of variations; Numerical treatment of solutions to differential equations and related optimization problems.

These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering.

This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002. Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT program.

This book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes. These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media, as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability distributions.

The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs. It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include a solid foundation in functional analysis and probability theory.