0
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1answer
16 views

characteristic equation in pde

In the PDE: $ yU_y-xU_x=1$ how did the characteristics become $dx\over -x$=$dy \over y$ =$du \over 1$.Can someone please expalin how these charactristic equations were obtained
1
vote
1answer
26 views

PDE $ u_{x}+u_{t}+f(x)*u=0$

How would I solve this pde using characteristic line? $u_{x}+u_{t}+f(x)u=0$---arbitrary function f $u(x,0)=u_{0}(x)$---$u_{0}$ can be any value $u(0,t)=\varphi(t)$---non-homogeneous where $u(x,t)\ge ...
0
votes
2answers
45 views

Finding the characteristic ODE from a nonlinear PDE

I am studying for a PDE exam on Tuesday, and I am getting pretty confused about one specific type of problem and I am thinking that perhaps I am misinterpreting the correct procedure to follow. The ...
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1answer
140 views

Burger's Equation 'Shocks' Not matching the characteristics

Album to view all the images that are described below. I have am using Burger's Equation with the initial condition of a Gaussian. The blue curve is the initial function before any time has passed, ...
2
votes
1answer
91 views

Show that the characteristic that passes through the point $(x,y)$ is given by $y(x)=\frac{1}{2}(x^{-2}-x_{0}^{-2})$

The function $u(x,y)$ satisfies the partial differential eqaution $x^{3}\frac{\partial u}{\partial x}-\frac{\partial u}{\partial y}=0$ Show that the characteristic that passes through the point ...