Applied and Numerical Partial Differential Equations

Standing at the intersection of mathematics and scientific computing, this collection of state-of-the-art papers in nonlinear PDEs examines their applications to subjects as diverse as dynamical systems, computational mechanics, and the mathematics of finance.

The present volume is comprised of contributions solicited from invitees to conferences held at the University of Houston, Jyväskylä University, and Xi'an Jiaotong University honoring the 70th birthday of Professor Roland Glowinski. Although scientists convened on three different continents, the Editors prefer to view the meetings as single event. The three locales signify the fact Roland has friends, collaborators and admirers across the globe.

The contents span a wide range of topics in contemporary applied mathematics ranging from population dynamics, to electromagnetics, to fluid mechanics, to the mathematics of finance. However, they do not fully reflect the breath and diversity of Roland's scientific interest. His work has always been at the intersection mathematics and scientific computing and their application to mechanics, physics, engineering sciences and more recently biology. He has made seminal contributions in the areas of methods for science computation, fluid mechanics, numerical controls for distributed parameter systems, and solid and structural mechanics as well as shape optimization, stellar motion, electron transport, and semiconductor modeling. Two central themes arise from the corpus of Roland's work. The first is that numerical methods should take advantage of the mathematical properties of the model. They should be portable and computable with computing resources of the foreseeable future as well as with contemporary resources. The second theme is that whenever possible one should validate numerical with experimental data.

The volume is written at an advanced scientific level and no effort has been made to make it self contained. It is intended to be of interested to both the researcher and the practitioner as well advanced students in computational and applied mathematics, computational science and engineers and engineering.

State of the art in advanced mathematical modelling and simulation methods Domain specific innovations in acoustics, computational mechanics, electromagnetics, mathematical finance, biomedical engineering, and population biology A multidisciplinary approach

Contenu
Roland Glowinski: The Unconventional and Unexpected Path of a Mathematician.- The Scientific Career of Roland Glowinski.- On a Class of Partial Differential Equations with Nonlocal Dirichlet Boundary Conditions.- A Unified Discrete#x2013;Continuous Sensitivity Analysis Method for Shape Optimization.- A Novel Approach to Modeling Coronary Stents Using a Slender Curved Rod Model: A Comparison Between Fractured Xience-Like and Palmaz-Like Stents.- On the Stochastic Modelling of Interacting Populations. A Multiscale Approach Leading to Hybrid Models.- Remarks on the Controllability of Some Parabolic Equations and Systems.- Goal Oriented Mesh Adaptivity for Mixed Control-State Constrained Elliptic Optimal Control Problems.- Feedback Solution and Receding Horizon Control Synthesis for a Class of Quantum Control Problems.- Fluid Dynamics of Mixtures of Incompressible Miscible Liquids.- Demand Forecasting Method Based on Stochastic Processes and Its Validation Using Real-World Data.- Analytic Bounds for Diagonal Elements of Functions of Matrices.- Numerical Methods for Ferromagnetic Plates.- Two-Sided Estimates of the Solution Set for the Reaction#x2013;Diffusion Problem with Uncertain Data.- Guaranteed Error Bounds for Conforming Approximations of a Maxwell Type Problem.- A Componentwise Splitting Method for Pricing American Options Under the Bates Model.- Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach.