Methods for Partial Differential Equations Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models /
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the "research project for beginners" proposed at the end of the book. It is a valuable resource for...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing,
2018.
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| Edition: | 1st ed. 2018. |
| Subjects: | |
| ISBN: | 9783319664569 |
| Online Access: |
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Table of Contents:
- Part 1
- Introduction
- Part 2
- Partial differential equations in models
- Basics for partial differential equations
- The Cauchy-Kovalevskaja theorem
- Holmgren's uniqueness theorem
- Method of characteristics
- Burger's equation
- Laplace equation - properties of solutions - starting point of elliptic theory
- Heat equation - properties of solutions - starting point of parabolic theory
- Wave equation - properties of solutions - starting point of hyperbolic theory
- Energies of solutions - one of the most important quantities
- Part 3
- Phase space analysis for heat equation
- Phase space analysis and smoothing for Schrödinger equations
- Phase space analysis for wave models
- Phase space analysis for plate models
- The method of stationary phase and applications
- Part 4
- Semilinear heat models
- Semilinear classical damped wave models
- Semilinear wave models with a special structural dissipation
- Semilinear classical wave models
- Semilinear Schrödinger models
- Linear hyperbolic systems
- Part 5
- Research projects for beginners
- Background material.