Continuous and Distributed Systems: Theory and Applications

✍ Scribed by Anatoly T. Fomenko, Andrei Konyaev (auth.), Mikhail Z. Zgurovsky, Victor A. Sadovnichiy (eds.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 334
• Series: Solid Mechanics and Its Applications 211
• Edition: 1
• Category: Library

✦ Synopsis

In this volume, the authors close the gap between abstract mathematical approaches, such as abstract algebra, number theory, nonlinear functional analysis, partial differential equations, methods of nonlinear and multi-valued analysis, on the one hand, and practical applications in nonlinear mechanics, decision making theory and control theory on the other.

Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in hydromechanics, geophysics and mechanics of continua. This compilation will be of interest to mathematicians and engineers working at the interface of these field. It presents selected works of the open seminar series of Lomonosov Moscow State University and the National Technical University of Ukraine “Kyiv Polytechnic Institute”. The authors come from Germany, Italy, Spain, Russia, Ukraine, and the USA.

✦ Table of Contents

Front Matter....Pages i-xix
Front Matter....Pages 1-1
Algebra and Geometry Through Hamiltonian Systems....Pages 3-21
On Hyperbolic Zeta Function of Lattices....Pages 23-62
The Distribution of Values of Arithmetic Functions....Pages 63-66
On the One Method of Constructing Digital Control System with Minimal Structure....Pages 67-71
On Norm Maps and “Universal Norms” of Formal Groups Over Integer Rings of Local Fields....Pages 73-80
Assignment of Factors Levels for Design of Experiments with Resource Constraints....Pages 81-86
Front Matter....Pages 87-87
How to Formulate the Initial-Boundary-Value Problem of Elastodynamics in Terms of Stresses?....Pages 89-95
Finite-Difference Method of Solution of the Shallow Water Equations on an Unstructured Mesh....Pages 97-113
Dynamics of Vortices in Near-Wall Flows with Irregular Boundaries....Pages 115-129
Strongly Convergent Algorithms for Variational Inequality Problem Over the Set of Solutions the Equilibrium Problems....Pages 131-146
Front Matter....Pages 147-147
Multivalued Dynamics of Solutions for Autonomous Operator Differential Equations in Strongest Topologies....Pages 149-162
Structure of Uniform Global Attractor for General Non-Autonomous Reaction-Diffusion System....Pages 163-180
Topological Properties of Strong Solutions for the 3D Navier-Stokes Equations....Pages 181-187
Inertial Manifolds and Spectral Gap Properties for Wave Equations with Weak and Strong Dissipation....Pages 189-203
On Regularity of All Weak Solutions and Their Attractors for Reaction-Diffusion Inclusion in Unbounded Domain....Pages 205-220
On Global Attractors for Autonomous Damped Wave Equation with Discontinuous Nonlinearity....Pages 221-237
Front Matter....Pages 239-239
On the Regularities of Mass Random Phenomena....Pages 241-250
Optimality Conditions for Partially Observable Markov Decision Processes....Pages 251-264
On Existence of Optimal Solutions to Boundary Control Problem for an Elastic Body with Quasistatic Evolution of Damage....Pages 265-286
On Existence and Attainability of Solutions to Optimal Control Problems in Coefficients for Degenerate Variational Inequalities of Monotone Type....Pages 287-301
Front Matter....Pages 239-239
Distributed Optimal Control in One Non-Self-Adjoint Boundary Value Problem....Pages 303-312
Guaranteed Safety Operation of Complex Engineering Systems....Pages 313-326
Back Matter....Pages 327-333

✦ Subjects

Theoretical and Applied Mechanics; Systems Theory, Control; Physical Chemistry