so i wonder the next thing : if i consider a pde like heat equation Fourier transform works very well. Now, if i consider this equation :
$\frac{\partial u(t,x)}{\partial t}-k(u(t,x))\frac{\partial^2 u(t,x)}{\partial x^2} = 0$
We see Fourier transform can't help us because of the non-linear term. That's why i would like what transform is the best, for instance Laplace transform ? I think no because in Laplace space the product does not become the convolution whereas with Fourier Transform it is. So what do you think about that ?
Thanks a lot !