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

### mohan (view profile)

on 11 Dec 2012

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

### Babak (view profile)

on 12 Dec 2012

• 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.

mohan

### mohan (view profile)

on 12 Dec 2012

**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

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