# Solve A*(Uxx+Uyy)-B(x)*Ux=0

1. Aug 15, 2005

### JG

I must solve A*(Uxx+Uyy)-B(x)*Ux=0 , where Uxx means ssecond partial derivative of U on x and U(x,y); Ais constant and B(x) is function of x! The eq has BC dU/dz=0 and dU/dy=0 IC U(0,y)=1 for -1<y<0 and U(0,y)=1 for 0<y<1 in Mathematica!
Can anybody help me with some example? Thanks, Jan mail: jan_golob@email.si

2. Aug 16, 2005

### saltydog

Hey JG, don't know why others aren't commenting about your problem but for me it is a bit awkwardly posed. This is what I would consider well-posed:

$$\text{DE:}\quad Au_{xx}+Au_{yy}-B(x)u_x=0\quad 0\le x \le L$$

$$\text{BC:}\quad u_x(0,t)=0\quad u_x(L,t)=0$$

$$\text{IC:}\quad u(x,0)=f(x)\quad u_t(x,0)=g(x)$$

Now saying that's yours but if the problem were this, then I'd use separation of variables and proceed.

Last edited: Aug 16, 2005