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This volume comprises selected papers from the 21st Conference on System Modeling and Optimization in Sophia Antipolis, France. It covers over three decades of studies involving partial differential systems and equations. Topics include: the modeling of continuous mechanics involving fixed boundary, control theory, shape optimization and moving boundaries, and topological shape optimization. This edition discusses all developments that lead to current moving boundary analysis and the stochastic approach.

Discussing developments that lead to current moving boundary analysis and the stochastic process, this book, developed from the proceeding of the 21st Conference on System Modeling and Optimization, explores over three decades of studies involving partial differential systems and equations. The book provides new existence results derived from fine analysis of boundary behavior, includes intrinsic geometry developed for shell modeling, introduces new algorithms associated with current computing power, allowing impressive simulations with particle flow, and contains a numerical treatment of the mathematical Speed Method or Eulerian parametrization tool.

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Operator-Splitting Methods and Application to the Direct Numerical Simulation of Particulate Flow and to the Solution of the Elliptic Monge-Ampere Equation. Dynamical Shape Sensitivity. Optimal Control of a Structural Acoustic Model with Flexible Curved Walls. Nonlinear Wave Equations with Degenerate Damping and Source Terms. Numerical Modeling of Phase Change Problems. Shape Optimization of Free Air-Porous Media Transmission Coefficient. The Uniform Fat Segment and Uniform Cusp Properties. Topology Optimization for Unilateral Problems. Second Order Lagrange Multiplier Approximation for Constrained Shape Optimization Problems. Mathematical Models of 'Active' Obstacles in Acoustic Scattering. Local Null controllability in a State Constrained Thermoelastic Contact Problem. On Sensitivity of Optimal Solutions to Control Problems for Hyperbolic Hemivariational Inequalities. Evolution Hemivariational Inequality with Hysteresis and Optimal Control Problem. On the Modeling and Control of Delamination  Processes. On a Spectral Variational Problem Arising in the Study of Earthquakes. Nodal Control of Conservation Laws on Networks. Invariance of Clossed Sets under Stochastic Control Systems. Uniform Stabilization of an Anisotropic System of Thermoelasticity. Well-Posedness of Multilayer Mead-Markus Plate with Shear Damping. Solution of Algebraic Riccati Equations Arising in control of Partial Differential Equations. Stabilization in Computing Saddle Points. Second Order sufficient Conditions for Optimal Control Subject to First Order State Constraints.

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