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February 28, 2004, 19:03 
exact solution of burger's equation

#1 
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can anyone help me getting exact solution of inviscid burger's equation?


February 29, 2004, 00:05 
Re: exact solution of burger's equation

#2 
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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 

February 29, 2004, 20:03 
Re: exact solution of burger's equation

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


March 1, 2004, 05:12 
Re: exact solution of burger's equation

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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. 

March 1, 2004, 09:07 
Re: exact solution of burger's equation

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


March 1, 2004, 09:32 
Re: exact solution of burger's equation

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The HopfCole 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.


March 1, 2004, 23:52 
Re: exact solution of burger's equation

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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 

March 1, 2004, 23:57 
Re: exact solution of burger's equation

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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 

March 3, 2004, 21:47 
Re: exact solution of burger's equation

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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.


March 4, 2004, 04:55 
Re: exact solution of burger's equation

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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.


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