Evolution Equations of Hyperbolic and Schrödinger Type [electronic resource] : Asymptotics, Estimates and Nonlinearities /
Ruzhansky, Michael.editor.
Sugimoto, Mitsuru.editor.
Wirth, Jens.editor.
Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates; and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and allows researchers as well as students to grasp new aspects and broaden their understanding of the area.
Description based upon print version of record.
Evolution Equations of Hyperbolic and Schrödinger Type; Asymptotics, Estimates and Nonlinearities; Contents; Preface; Divergence-type Operators: Spectral Theory and Spacetime Estimates; 1. Introduction; 2. Functional spaces and notation; 3. The basic abstract structure; 3.1. The limiting absorption principle - LAP; 3.2. Persistence of smoothness under functional operations; 4. The limiting absorption principle for second-order divergence-type operators; 4.1. The operator Ho =-Δ - revisited; 4.2. Proof of the LAP for the operator H
4.3. An application: Existence and completeness of the wave operators W±(H,Ho)5. An eigenfunction expansion theorem; 6. Global spacetime estimates for a generalized wave equation; References; Kinetic Models of Chemotaxis; 1. Introduction; 2. Strichartz and dispersion estimates for the kinetic transport equation; 3. Global existence for some kinetic models of chemotaxis; 4. Critical nonlinearities; 5. Blow-up in two dimensions; 6. Perspectives and open problems; Acknowledgment; References; Modulus of Continuity and Decay at Infinity in Evolution Equations with Real Characteristics
Acknowledgement References; Geometric Regularization on Riemannian and Lorentzian Manifolds; 1. Introduction; 2. Regularization of distributions on complete Riemannian manifolds; 2.1. Regularizations; 2.2. Finite speed of propagation; 2.3. Applications; 3. Regularization on globally hyperbolic space-times; 3.1. The metric splitting of globally hyperbolic space-times and associated Riemann metrics; 3.2. Regularization and embedding via the associated Riemannian structure; Acknowledgment; References
A Remark on the Uniqueness for Backward Parabolic Operators with non-Lipschitz-continuous Coefficients1. Introduction; 2. Main result; 3. Proof; 3.1. Weight function and Carleman estimate; 3.2. Littlewood-Paley decomposition, Bony's paramultiplication and commutators; 3.3. Carleman estimate and approximation; Acknowledgment; References; Dispersive Properties of Schrödinger Operators in the Absence of a Resonance at Zero Energy in 3D; 1. Introduction; 2. Resonance at the spectral origin; 3. Strong resonance at the spectral origin
4. The non-radial case: zero is resonance implies zero is an eigenvalue
Includes bibliographical references.
Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates; and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and allows researchers as well as students to grasp new aspects and broaden their understanding of the area.
Partial differential equations.
Operator theory.
Global analysis (Mathematics).
Manifolds (Mathematics).
Calculus of variations.
Partial Differential Equations.
Operator Theory.
Global Analysis and Analysis on Manifolds.
Calculus of Variations and Optimal Control; Optimization.