Modern Aspects of the Theory of Partial Differential Equations [electronic resource] /
Ruzhansky, Michael.editor.
Wirth, Jens.editor.
The book provides a quick overview of a wide range of active research areas in partial differential equations such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches. It will serve as a useful source of information to mathematicians, scientists and engineers. Contributors: Y.P. Apakov G. Avalos L. Bociu L. Boutet de Monvel F. Colombo G. Fragnelli M. Ghergu D. Guidetti U.U. Hrusheuski T.Sh. Kalmenov I.U. Khaydarov S. Khodjiev V. Kokilashvili C. Lebiedzik P. Loreti F. Macià D. Mugnai M. Reissig M.S. Salakhitdinov B.-W. Schulze D. Sforza L. Simon D. Suragan D. Toundykov R. Triggiani A.K. Urinov O.S. Zikirov J.-P. Zolésio.
Description based upon print version of record.
Modern Aspects of the Theory of Partial Differential Equations; Contents; Preface; Toeplitz Operators and Asymptotic Equivariant Index; 1. Szegö projectors, Toeplitz operators; 1.1. Example 1: Microlocal model; 1.2. Example 2: Holomorphic model; 1.3. Main properties; 1.4. Miscellaneous; 2. Equivariant Toeplitz algebra; 2.1. Equivariant trace; 2.2. Equivariant index; 2.3. Asymptotic index; 2.4. K-theory and embedding; 2.5. Embedding and transfer; 3. Relative index; 3.1. Enlargement; 3.2. Collar isomorphism; 3.3. Embedding; 3.4. Index; References
1.4. Norm growth estimates2. Operators on singular manifolds with conical exits; 2.1. Edge operator-valued amplitude functions; 2.2. Compositions; 2.3. Edge calculus up to infinity; 2.4. Ellipticity; References; On a Method for Solving Boundary Problems for a Third-order Equation with Multiple Characteristics; 1. Introduction; 2. Statement of the problem; 3. Uniqueness of the solution; 4. Existence of the solution; References; On Stability and Trace Regularity of Solutions to Reissner-Mindlin-Timoshenko Equations; 1. Introduction
1.1. Role of geometry and trace regularity in stabilization of PDE's1.2. Goals and challenges; 2. Reissner-Mindlin-Timoshenko (RMT) plate; 3. Trace regularity of solutions to RMT equations; 3.1. Elliptic region Re; 3.2. Hyperbolic region Rh; 3.3. Combined estimates; References; Linearization of a Coupled System of Nonlinear Elasticity and Viscous Fluid; 1. Introduction; 1.1. The problem and the model; 1.2. Notation; 1.3. PDE model; 1.4. Special case: Potential fluid; 1.5. Parameter of variation s; 2. Main results; 3. Preliminaries; 3.1. The moving boundary Γs
3.2. Transport of scalar operators
Includes bibliographical references.
The book provides a quick overview of a wide range of active research areas in partial differential equations such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches. It will serve as a useful source of information to mathematicians, scientists and engineers. Contributors: Y.P. Apakov G. Avalos L. Bociu L. Boutet de Monvel F. Colombo G. Fragnelli M. Ghergu D. Guidetti U.U. Hrusheuski T.Sh. Kalmenov I.U. Khaydarov S. Khodjiev V. Kokilashvili C. Lebiedzik P. Loreti F. Macià D. Mugnai M. Reissig M.S. Salakhitdinov B.-W. Schulze D. Sforza L. Simon D. Suragan D. Toundykov R. Triggiani A.K. Urinov O.S. Zikirov J.-P. Zolésio.
Mathematical analysis.
Analysis (Mathematics).
Partial differential equations.
Analysis.
Partial Differential Equations.
Operator theory