Analysis of singularities for partial differential equations 1st Edition by Chen Shuxing ISBN 9789814304832 by Chen S. 9789814304832, 9814304832 instant download after payment.

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ISBN 13: 9789814304832
Author: Chen Shuxing

The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.

Analysis of singularities for partial differential equations 1st Table of contents:

1. Introduction to problems on singularity analysis
1.1 The classical singularity propagation theorem
1.2 Towards to modern theory
2. Singularity analysis for linear equations
2.1 Wave front set
2.2 Singularity propagation theorem for equations of principal type
2.3 Reection of singularity on boundary
2.4 Further discussions
2.4.1 Generalized reection of singularity on boundary
2.4.2 The operators with multiple characteristics
3. Singularity analysis for semilinear equations
3.1 Theorem of propagation of 2s weak singularity
3.2 Theorem on propagation of 3s weak singularity
3.3 Singularity interaction and singularity index
3.4 Propagation of conormal singularity
3.5 Interaction of conormal singularities
3.5.1 Extension of the concept of conormal singularities
3.5.2 Pseudo-composition
3.5.3 Theorem on interaction of conormal singularities
3.5.4 Reection of conormal singularities
4. Propagation of singularities for fully nonlinear equations
4.1 Theorem of propagation of singularities for principal type equations
4.2 Propagation of conormal singularities for nonlinear equations
5. Propagation of strong singularities for nonlinear equations
5.1 Solutions with fan-shaped singularity structure of semilinear equations
5.2 Solutions with ower-shaped singularity structure of semilinear equations
5.3 Solutions with strong singularities of quasilinear equations (1-d case)
5.4 Solutions with strong singulari ties of quasilinear equations (m-d case)
5.4.1 Fan-shaped singularity structure
5.4.2 Flower-shaped singularity structure
6. Formation of shocks for quasilinear hyperbolic equations
6.1 The case of scalar equation
6.1.1 Two mechanism of blow-up of smooth solutions
6.1.2 Formation of a shock
6.1.3 Estimates of the solution in the neighborhood of the starting point of shock
6.2 The case of system
6.2.1 Background and conclusion
6.2.2 The property of the first approximate solution
6.2.3 Estimates and convergence of the sequence of approximate solutions
6.2.4 The case for full Euler system

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Tags: Chen Shuxing, Analysis, singularities