日本語訳が末尾にあります．

§0 and §1.1−1.2

• For basic linear PDEs (the diffusion equation, Poisson’s equation, the wave equation), read [Fa82] for more information on their physical meaning. For nonlinear equations, see [Ma07] for example.

§1.3−1.4

• To review the basics of Fourier transforms, read [SS02].
• For basic results on the linear heat equation, read [Ev10, §2.3] for more details (in particular the proof of the strong maximum principle [Ev10, §2.3.3]).

§2

• A general reference for this section is [松西04].
• For integrals of Banach space-valued functions, see [宮島05, §3.4] or [Le17, §8].
• To learn further about Sobolev spaces, I could recommend going through [宮島06] or [Le17].
• For the proof of $L^{\infty}$-norm blow-up, see [柳田15, Theorem 3.2].

§3

• For Perron’s method, see [GT01, Ch. 1 and 2].
• If you want to learn more about the calculus of variations, you could consult [Da14; Ev10, Ch. 8].

§4

• The treatment of Burgers’ equation in this lecture is in large part based on [Ev10, Ch. 3].

References

[Da14] B. Dacorogna, Introduction to the Calculus of Variations, Imperial College Press, 2014 (3rd ed).

[Ev10] L. C. Evans, Partial Differential Equations, American Mathematical Society, 2010 (2nd ed).

[Fa82] S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publication, 1982.