Bruce
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hi, all great brains, I have a question about BVP, which confused me a while, maybe someone can help to clarify it.
For a point source with Dirichlet boundary in a 2D domain, the response at any coordinate except the source point is dependent on the surface of the source, for example, heat transfer. But a point source, in theory has no surface in a 2D domain. So the transient solution with Dirichlet point source in a 2D domain is regarded as ill-defined problem(the solution has a singularity at source)? or it can be regarded as a weak form, are there any reference about this? or something is else wrong.
Just use the heat transfer as an example:
d(dT/dx)+d(dT/dy)=dT/dt
BC: T'(0,y,t)=T'(L,y,t)=T'(x,0,t)=T'(x,M,t)=0 ; 0<x<L;0<y<M;
IC: T(x,y,0)=delta(x-x',y-y',t-t') * T0thanks in advance.
Bruce
For a point source with Dirichlet boundary in a 2D domain, the response at any coordinate except the source point is dependent on the surface of the source, for example, heat transfer. But a point source, in theory has no surface in a 2D domain. So the transient solution with Dirichlet point source in a 2D domain is regarded as ill-defined problem(the solution has a singularity at source)? or it can be regarded as a weak form, are there any reference about this? or something is else wrong.
Just use the heat transfer as an example:
d(dT/dx)+d(dT/dy)=dT/dt
BC: T'(0,y,t)=T'(L,y,t)=T'(x,0,t)=T'(x,M,t)=0 ; 0<x<L;0<y<M;
IC: T(x,y,0)=delta(x-x',y-y',t-t') * T0thanks in advance.
Bruce