I have 1D diffusion (u(t,x)) PDE with Dirac Delta initial condition.
Question is regarding it's implementation:
Dirac delta func is formally defined as an encapsulation of 2 conditions:
1st condn: function takes value 1 at x=0,
2nd condition:function takes value 0, if x not equal to 0).
Thus, to solve the above PDE for initial condition u(t=0,x)=Dirac_delta(x), is it necessary to treat this dirac delta function initial condition (for that PDE) as ONE or TWO separate conditions (viz. after substituting for t=0 and x=0 giving u(t=0,x=0)=1 solution giving 1st equation for initial condition & substituting t=0 and x=x(i.e non-zero x) giving u(t=0,x)=0 giving 2nd equation for initial condition)??
This means, 1D diffusion PDE with Dirac Delta function (delta(x)) has 1 OR 2 initial conditions, according to for t=0, (x=0 & x not equal to 0)?