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partial differential equation

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See the attached file.

D(phi)/d(tau)+d(phi)/d(chi)+d(phi)/d(epsilon)+1=0
Boundary conditions:
phi as a f(chi,epsilon,0)=0
phi as a f(0,epsilon,tau)=1
phi as a f(chi,0,tau)=1
Solve the PDE..... solution and explanation would be fine
Any method to solving the solution would be fine
(numerical or analytical).

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Solution Summary

A partial differential equation is explored.

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