I am trying to solve a second order parabolic PDE using the method of characteristics. The PDE has the following form:

$$\alpha\frac{\partial^2u}{\partial x^2}-\gamma\frac{\partial u}{\partial x}-\frac{\partial u}{\partial y}-f(u(x,y))=0.$$ where $\alpha$ and $\gamma$ are constants and $f$ is a non-linear function.

If I follow the standard procedure, I have to build $\Delta=b^2-ac=0$ which shows the PDE is parabolic. $$\Rightarrow \frac{dy}{dx}=\frac{b+\sqrt{\Delta}}{a}=0$$ Now it seems that no new variable can be chosen. Do you any idea how this problem can be solved...?

Thanks in advance


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.