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I've been trying recently to solve the following system of Hamilton-Jacobi PDE's, which are of the hyperbolic, first-order type:

$ V_1,_t - 0.5 V_1,_x^2 + V_1,_x(0.1x^2+0.03x+.0.01)+0.02(x-0.5)^2-V_1,_x V_2,_x=0$
$ V_2,_t - 0.5 V_2,_x^2 + V_2,_x(0.1x^2+0.03x+.0.01)+0.03(x-0.5)^2-V_1,_x V_2,_x=0 $
With terminal time conditions: $V_1(T,x)=0, V_2(T,x)=0$, where T is some final time and x is scalar.

I need to solve it only numerically, get some plots for the two Value Functions and done! The problem is I couldn't solve it in Mathematica, and I'm having trouble with MATLAB as the PDEtoolbox seems to not let me choose a terminal time condition.

Also I'm not that experienced in solving this kind of problems in any software. However I have available a couple different software so if anyone could give me some help and guidelines in any known software and in order to solve it I would be in debt!
Cheers!

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  • $\begingroup$ It is very unlikely that someone is going to write your code for you. If the issue is with programming rather than math, then you should close this and ask a more specific question at StackOverflow.com/Matlab (or possibly SciComp.StackExchange.com). Be sure to show the code you've written and point out exactly where the problem is. $\endgroup$ – horchler Nov 13 '15 at 23:39
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Unless I'm missing something, you can just integrate backwards in time, starting at t=T. Do this by introducing a new variable t'=T-t and then your problem becomes a normal integration with a given starting condition of V1=V2=0, for all x.

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