how to solve PDE with variable coefficients and give step to these variable coefficients

I have a PDE equation with variable coefficients

    Ut-Uxx= P(t)

Boundary condition

        U(0,t) = 0

        Ux(x,t) =  -sig(t)/eta

initial condition

            U(x2,0) = P_*x*(H-x)

Ut is partial diff w.r.t t Uxx is partial diff w.r.t x

P(t) is function of t ,eta is constant ,H is constant

sig(t) is a function of t

How to solve the PDE equation and after solvint the equation i need to give step input to P(t) and sig(t)

[Babak]

Please clarify these:

• Do you mean Ux(L,t) =... as for the boundary condition?
• What is the specific function for sig(t)? Or is it a general function of time?
• What is P_? is it same as P? if not please specify!
• What do you mean by U(x2,0)? Do you mean U(x,0)? If so, please correct it.

Please correct the typos or they will confuse the whole crowd who are here only to help you answering your question!

[mohan]

**yes it is Ux(L,t)

sig(t) is a function of time ...

P_ is constant and not same as P . U(x2,0) = U(x,0)

P(t) and sig(t) are step inputs

i have to solve for 2 cases i.e how the pde is varying for the two case's below

first case .. P(t)= 7*stepfunction and sig(t)= 0

second case...P(t)=0 and sig(t)= step function