Transport Equation IVP Solution

  • Thread starter Thread starter Robconway
  • Start date Start date
  • Tags Tags
    Pde Transport
Robconway
Messages
4
Reaction score
0

Homework Statement



Hi guys, I'm having trouble with a homework problem:

I will have to solve for the IVP of a transport equation on R:

the equations are:

Ut-4Ux=t^2 for t>0, XER
u=cosx for t=0, XER




Homework Equations



transport equation

The Attempt at a Solution




This non-linear transport solution is throwing me off. I don't know if I am supposed to use D'alemberts(As I have been doing for my previous HW problems)
Also, I can't directly solve for the homogeneous equation which in turn makes the u=cos x part very hard to solve
 
Physics news on Phys.org

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

PDE for IVP on R for a transport equation
Replies
2
Views
2K
Avoid unpleasant integrals in solving IVP
Replies
3
Views
2K
Model CO2 diffusing across the wall of a cylindrical alveolar blood vessel
Replies
0
Views
1K
PDE and the separation of variables
Replies
11
Views
1K
Solving modified heat equation
Replies
5
Views
975
Solve the given first order PDE
Replies
5
Views
2K
Solve the given first order Partial differential equation.
Replies
1
Views
862
Solving the wave equation with piecewise initial conditions
Replies
11
Views
2K
Is there a solution to this simple 1st order PDE?
Replies
16
Views
1K
How to get general solution via Green's function?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top