Request for Hints to solve a Non-Linear PDE

[mohammad449]

Dear Friends,
Would you please provide me with some hints to find the analytical solution of the non-linear PDE given below:
U=U(z,t)

Uzz-(A/U)*Uz=Ut

BC's and IC's are:
U(z,0)=B
U(1,t)=B
Uz(0,t)=A*H(t); "H" is the heaviside function and H(0)=0

where A, B, and C are constant.


Many Thanks,

 

[JJacquelin]

Hi !

Since there is no answer yet to the question, I dare give my opinion on the subject.
The analytical solutions of most of the non-linear PDE are not known. The solutions of only a few of them can be formally expressed (generally in case of school problems). In practice, numerical methods are used to treat the problems involving PDE in physics or industry.
I think that the mohammad449's non-linear PDE should be treated with a numerical software.
Nevertheless, I hope that someone will give a more theoretical answer.

 

[mohammad449]

Thanks so much Dear JJacquelin!

Actually, the original equation has been simplified to the given form. I have the numerical results of the original complicated equation.
Currently, I am trying to find an analytical solution to match the numerical one. I tried the Heat Integral method (to get an approximation) but the resulting solution was not accurate enough, it just works in some specific conditions.