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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.

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  • $\begingroup$ This would be a good candidate for a Laplace tranform, however you may have a tricky inverse transform to deal with. $\endgroup$ – DaveNine Jan 16 at 20:45
  • $\begingroup$ Thanks for your answer, i will try. $\endgroup$ – Pham Van Hien Jan 17 at 4:15
  • $\begingroup$ Since this is nonlinear, and you’re considering an IVBP, there may not be an explicit solution anyways. Can you provide more background to the problem? $\endgroup$ – DaveNine Jan 17 at 19:06

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