We can construct the solutions of semi-linear partial differential eqations by Riesz Representation theorem. We don't consider the initial conditions or smoothness but consider the boundary conditions. The comparisons with previous researches are on [4].
I am trying to understand whether there is a conceptual way to motivate generalized-function solution theories for PDEs that is analogous to the way gerbes with connection arise from integration ...
I took grad level PDE in 1979! I decided to dig up my class notes and textbook,
(Fritz John, 3rd ed) and do some work by studying (again) and learning what I did over 45 years ago. I found the book to ...
[These are notes intended mostly for myself, as these topics are useful in random matrix theory, but may be of interest to some readers also. -T.] One of the most fundamental partial differential equations in mathematics is the heat equation where is a scalar function of both time and space, and is the Laplacian . […]
