0
$\begingroup$

we have the following problem $$ \dfrac{\partial u}{\partial t} - \Delta u + F(u)= f(x,t); t >0, x \in \mathbb{R}^n; \ u(x,0)=0 $$ where $F$ is n linear, lipchitzian increazing function.

My question is how we prouve the existence of solution of this problem using Fadeo Galerkin method? I learn books but i don't found application of Fadeo Galerkin in the general case when F is no linear.

Thank's in advance to the help

$\endgroup$
0
$\begingroup$

You can find it in PDEs book of L. C. Evans.

$\endgroup$
  • $\begingroup$ partial differential equations lawrence c. evans $\endgroup$ – Trần Quang Minh Jun 14 '18 at 10:52
  • $\begingroup$ I have this book but i don't see my problem with general non linear function F. In wich page we can fund it? Plesase. I have the book who's in the following link: libgen.pw/item/adv/5a1f046d3a044650f5faacc5 $\endgroup$ – mati Jun 14 '18 at 10:59
  • $\begingroup$ Can you help me please $\endgroup$ – mati Jun 14 '18 at 14:26
0
$\begingroup$

In this case, you can not apply the Faedo-Galerkin method, it is not applicable in a free domain $\mathbb{R}^n$, the spectrum of the Laplacian is not discrete, in your case, there is no eigenvalues and eigenvectors of the Laplacian you can not make the approximation.

$\endgroup$

Your Answer

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

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