Nonlinear Theory of Generalized Functions

ISBN-13: 9781138417748 / Angielski / Twarda / 2020

Michael Oberguggenberger; Peter J. Olver; Michael Grosser

Opis

Covers the research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this work provides a compilation of approaches to the problem of singularities in nonlinear models.

Spis treści

Partial Differential Equations On the Structure of Singularities in Solutions of the Nonlinear Schroedinger Equation for the Critical Case, p = 4/n , The Schroedinger Equation with Point Interaction in an Algebra of New Generalized Functions, Polynomial a Priori Estimates for Some Evolution PDE and Generalized Solutions, Shift Differentials of Maps in BV Spaces, Calculation of the Singularity Dynamics for Quadratic Nonlinear Hyperbolic Equations. Example: The Hopf Equation, Vanishing Viscosity Boundary Layers for Nonlinear Hyperbolic Systems, Ordinary Differential Equations and Generalized Functions, Conservation Laws, Delta Shocks and Singular Shocks, Nonlinear Singular Schroedinger Type Equations, H. Lange, m. Poppenberg, Non-Analytic Solutions of Nonlinear Wave Models, The Dirichlet Problem and Compact Operators in Colombeau Theory, Highly Oscillatory Shock Waves, Structure Theory Sharp Topologies on (C, E, P)-Algebras, (C, E, P)-Sheaf Structures and Applications, Local and Microlocal Analysis in the Space of Colombeau Generalized Functions, Basics of a General Spectral Theory of Banach Modules, Extensions of Algebras, Memofunctions and Their Applications, On the Multiplication of Periodic Hyperfunctions of One Variable, Geometry, General Relativity Distributional Aspects of General Relativity: The Example of the Energy-Momentum Tensor of the Extended Kerr-Geometry, Lie Symmetries of Differential Equations in a Generalized Functions Setting, Arbitrary Global Lie Group Actions on Generalized Solutions of Nonlinear PDEs and an Answer to Hilbert's Fifth Problem, Distributional Description of Impulsive Gravitational Waves, Non-Linear Generalized Functions in General Relativity, Stochastic Analysis A White Noise Approach to Stochastic Differential Equations Driven by Wiener and Poisson Processes, H. Holden, B. White Noise Driven Stochastic Partial Differential Equations: Triviality and Non-Triviality, F. Russo, Measurement Methods Related to Differential Equations, On the Small Time Asymptotics of Solutions of Linear and Non-Linear Stochastic Differential Equations, Nonstandard Methods The Global Control of Shock Waves, Pointwise Values and Fundamental Theorem in the Algebra of Asymptotic Functions

O autorze

Michael Oberguggenberger (Inst Mathematic/Geometrie, Innsbruck, Austria) (Edited by) Michael Grosser (University of Vienna, Vienna, Austria) (Edited by) Michael Kunzinger (Edited by) Gunther Hormann (Institut fur Mathematic, Vienna, Austria) (Edited by)