exact solution of burger's equation
 

can anyone help me getting exact solution of inviscid burger's equation?

Re: exact solution of burger's equation
 

For u_t + u u_x =0

we get

u(x,t)=f(x - u(x,t)t) for any f(x). which gives us an implicit solution for u(x,t) but this solution can be used to obtain a slope in order to check the change of u wrt "x".

Hope this helps

Re: exact solution of burger's equation
 

hey rvndr i did not get exactly what you write. can u plz elaborate.

Re: exact solution of burger's equation
 

The characteristics of the Burger equation satisfy

dt/ds = 1, dx/ds = u, du/ds = 0

where s is a parameter along the characteristic. Initially (s=0) set

t = 0, x= z, u=f(z),

then we have (t=s)

u=f(z), x = z + tf(z)

Tom.

Re: exact solution of burger's equation
 

You can also solve it using a Cole-Hopf transformation. Try doing a search on google for Cole-Hopf and burger's equation.

Re: exact solution of burger's equation
 

The Hopf-Cole transformation is for the viscous problem and doesn't work in the inviscid case - unless you are suggesting solving the viscous problem exactly and then taking the limit of zero viscosity.

Re: exact solution of burger's equation
 

hi sajar,

Tom explained it nicely. Still if you have doubt post that PDE and let me solve that euation for you if I can.

rvndr

Re: exact solution of burger's equation
 

hi sajar,

Tom explained it nicely. Still if you have doubt post that PDE for which you want to know the exact solution and let me solve that euation for you if I can.

rvndr

Re: exact solution of burger's equation
 

The viscous and inviscid Burger's equations display markedly different dynamics in the shock region - are you sure that you can get to the inviscid solution with such a limiting process? I would guess not, but I haven't actually done it.

Re: exact solution of burger's equation
 

Yes you can - it's simple matched asymptotic expansions (see the book by Kevorkian and Cole and also Whitham's book on linear and nonlinear waves). Basically this is how shock capturing methods work in numerical models.