Reference: Fourier transform and applications to finding solutions and deriving estimates for PDEs

Question

I'm looking for books or sets of lecture notes where that show examples (worked out in detail) of applications of Fourier transform techniques to PDE to find explicit expressions of solutions, well-posedness and estimates (for example in $L^p$ norms).

I'm particularly interested in applications to classical equations like

1. heat equation;
2. Laplace equation;
3. wave equation;
4. Schroedinger equation;
5. telegraph equation;
6. damped wave equation.

Please, in your answers, along with a reference, include the number corresponding to the equation covered.

Answer 1

Undergraduate level: Walter Strauss, PDE.

Graduate level: Lawrence Evans, PDE.