Methods for Partial Differential Equations Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models
Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the ran...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2018, 2018
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| Edition: | 1st ed. 2018 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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