Question

PDE question

Answer 1

@ganeshie8 @IrishBoy123

Answer 2

What the heck is all that?

Answer 3

It looks as if somebody was having a sneeze fit while trying to write a normal problem.

Answer 4

hey astro

i had a quick look at it yesterday or day before, and saw this:
https://en.wikipedia.org/wiki/Heat_kernel

.... but they want an integral representation and that looks involved and quite a specialised piece of knowledge....to me at least :-((

suspect you know all of that already, though !

Answer 5

thank you for interest..

Answer 6

How about these ones

Answer 7

for the heat equation, we can apply the \(separation\;of\;variables\) method, namely I write the unknown function \(u(x,t)\) as a product of two functions, like below:
\[\huge u\left( {x,t} \right) = X\left( x \right) \cdot T\left( t \right)\]
where function \(X\) depends on \(x\) only, and similarly, function \(T\) depends on \(t\) only