the heat equation with solution-dependent coefficients

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I meet the problem

$$u_t(t,x)=\frac{A}{B-u}u_{xx}(t,x)$$

with the boundary conditions:

$$u(0,x)=B, x\in[0,H]$$ $$u(t,0)=u(t,H)=0, t>0$$ $$u(+\infty,x)=0$$

I have not any idea to start. Can you help me please.