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to find the exact solution of 1D Burges Equation |
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May 11, 2003, 06:17 |
to find the exact solution of 1D Burges Equation
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#1 |
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the Eq. u,t+u*u,x=0 u(x,0)=alpha+Pi*sin(Pi*x),-1<x<1
the analytic solution? thanks! |
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May 12, 2003, 05:33 |
Re: to find the exact solution of 1D Burges Equati
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#2 |
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If you mean the inviscid burgers equation (u_t + uu_x =0) then the solution is, parametrically,
u = U(s) = alpha + pi.sin(pi.s), x = s + t.U(s) |
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May 12, 2003, 09:13 |
Re: to find the exact solution of 1D Burges Equati
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#3 |
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Dear Tom, Thanks a lot for your solution.Yeah,I just need the solution of inviscid burgers equation.I am sorry that I had given a poor expression of my issue. Your reply is of much help for me,but could you give me a detailed explaination for me. I can't understand meanings of 's'and 'U(s)'. Thanks Again!
Yours sincerely Tian Baolin |
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May 13, 2003, 05:34 |
Re: to find the exact solution of 1D Burges Equati
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#4 |
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s is simply a parameter if you fix t and vary s you get the values of u and corresponding values x. Another way of looking at it is to think os s as a Langrangian marker for a fluid particle. If you fix s and vary time the value of u does not change and so is equal to it's initial value U(s) while it's position (x=s at t=0) has changed due to convection.
Hope this helps - you may want to look at the book "Linear and Nonlinear Waves" by G.B. Whitham which discusses the Burger equation in detail, Tom. |
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