(Solved): 10 points) Heres an important formula in PDE theory: u(x, t) = 1 2t f (y)e ...

10 points) Here’s an important formula in PDE theory:
u(x, t) = 1
2???t
? ?
??
f (y)e?(x?y)2/(4?t)dy.
(a) (4 pts) What name(s) does this formula have? (One name is
enough.)
(b) (6 pts) Which equation that we have studied in class does u
solve? For full credit, write down the corresponding PDE, the
auxiliary conditions that match this solution, and the domain in
which the solution is valid.

(10 points) Here's an important formula in PDE theory: $u(x,t)=\frac{1}{2\sqrt{??t}}{?}_{??}^{?}f(y)e^{?(x?y{)}^2/(4?t)}dy$ (a) (4 pts) What name(s) does this formula have? (One name is enough.) (b) (6 pts) Which equation that we have studied in class does $u$ solve? For full credit, write down the corresponding PDE, the auxiliary conditions that match this solution, and the domain in which the solution is valid.