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I have a few questions on the history of PDE.

1. Who first wrote down the formula for the solution of the Cauchy problem for the heat equation involving the heat kernel? I have seen it called Poisson's formula. If it is true Poisson has a formula for each of the heat, wave, and Laplace equations.
2. Who is the discoverer of the analogous formula for the wave equation in 2 and 3 dimensions? I have seen they were called both Kirchhoff's formula and Poisson's formula.
3. Is there a book to look up such questions? I have Dieudonne's Hisoty History of functional analysis, but it does not have much on PDEs other than the Laplace equation.
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# History of fundamental solutions

I have a few questions on the history of PDE.

1. Who first wrote down the formula for the solution of the Cauchy problem for the heat equation involving the heat kernel? I have seen it called Poisson's formula. If it is true Poisson has a formula for each of the heat, wave, and Laplace equations.
2. Who is the discoverer of the analogous formula for the wave equation in 2 and 3 dimensions? I have seen they were called both Kirchhoff's formula and Poisson's formula.
3. Is there a book to look up such questions? I have Dieudonne's Hisoty of functional analysis, but it does not have much on PDEs other than the Laplace equation.