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free boundary problem
Hi, i'm trying to get a numerical solution to a free boundary problem in mathematica. In general it looks like this: LV(x,t)=dV(x,t) on the area where 0 <= x <= b(t) V(x,t)=x on the rest dV(x,t)/dx = 1 for x=b(t) with some other "non-free" boundary conditions. The L stands for a differential operator in x, the d for differentation w.r.t. t. Furthermore the free boundary b(t) is defined as the minimum over the t >=0 for which V(x,t)=x. I'd appreciate any suggestions! Anybody an idea how to tackle this? Thanks in advance!