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For example I have a PDE with the dependent variable $u$ and the independent variables $x$ and $y$ . Suppose I have the change of variables that $v=u_x$ , I know the condition of $u(x,a)=f(x)$ will change to the condition of $v(x,a)=f_x(x)$ .

But when the condition is for example of the form $u(f(x),g(x))=h(x)$ , applying the change of variables that $v=u_x$ , the condition will change to what?

doraemonpaul
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  • Hi, @doraemonpaul could you help me to check the question and further elaborate the derivation process you briefly mentioned several days ago at this stackexchange page link. I tried my own my method to use the residue theorem, but it is difficult to get a closed-form solution for the higher derivatives, so I am wondering whether you have a better method to get the final result. Thanks a lot in advance. – Vic Oct 24 '15 at 15:16

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