Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have some problem to find a method to solve the following $PDE$: $$\partial_t ln[u(x,t)]=k^2\partial_{xx}u(x,t)$$ The equations resembles a common heat equation, but the logarithm of the function $u(x,t)$ seems to complicate the solution. Does someone have hints or answer? Many thanks.

share|improve this question
    
Does your PDE equivalent to $\partial_tu(x,t)=k^2u(x,t)\partial_{xx}u(x,t)$ ? –  doraemonpaul Nov 12 '12 at 2:43

1 Answer 1

up vote 0 down vote accepted

If you try to write a solution as a complex Fourier Series, this should break down to a series expansion of $ax+b$. Of course, you will need two boundary conditions to fully solve the equation.

share|improve this answer
    
This is nonlinear 2nd order PDE. I don't think writing the solution as a complex Fourier Series is easy. –  doraemonpaul Jul 9 '12 at 8:33

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.