Register to reply 
Finding a solution of this PDEby climbon
Tags: solution 
Share this thread: 
#1
Jul2811, 06:33 AM

P: 17

Hi,
i'm having trouble finding a solution to this PDE, [tex] \frac{d U(x,y,t)}{dt} = A(x) \frac{\partial U(x,y,t)}{\partial y} + B(y) \frac{\partial U(x,y,t)}{\partial x}[/tex] with only knowledge of the initial condition U(x,y,0)=F(x,y). I've tried to solve this using characteristics but the only examples i can find in books is for the case when the left hand side is zero. Tried following the method from some books but can only solve it for when the L.H.S is zero. I'm not sure where to go next Any help would be fantastic. Thanks. 


#2
Jul2811, 12:52 PM

HW Helper
P: 1,583

For the LHS do you mean:
[tex] \frac{\partial U}{\partial t} [/tex] 


#3
Jul2811, 08:13 PM

P: 85

Then, for (parameter) s∈I⊂ℝ: d/ds[U(x(s),y(s),t(s))]= ∂U/∂x·dx/ds + ∂U/∂y·dy/ds + ∂U/∂t·dt/ds≡ B(y)∂U/∂x + A(x)∂U/∂y  ∂U/∂t= 0. You seek, U(x(s),y(s),t(s))= constant. ADDENDUM: Hint: dx/B = dy/A = dt/1. 


Register to reply 
Related Discussions  
Please help me in finding a solution  Precalculus Mathematics Homework  5  
Finding solution of a PDE  Calculus & Beyond Homework  4  
Finding a solution to this?  Calculus  8  
Finding a solution?  Introductory Physics Homework  4 