Methods for partial differential equations : qualitative properties of solutions, phase space analysis, semilinear models / Marcelo R. Ebert, Michael Reissig.

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.