I am looking for a text or answer detailing the blowup of solutions to parabolic PDE (eg. heat equation) in Sobolev space setting. I heard blowup is related to size of domain but I can't find any nice text explaining this. I'd like to see the calculations done, preferably with Galerkin method if appropriate.

Thanks.

(CP from http://math.stackexchange.com/questions/483922/blow-up-of-solutions-to-parabolic-pde as I didn't get any attention)

I am looking for a text or answer detailing the blowup of solutions to parabolic PDE (eg. heat equation) in Sobolev space setting. I heard blowup is related to size of domain but I can't find any nice text explaining this. I'd like to see the calculations done, preferably with Galerkin method if appropriate.

Thanks.

(CP from https://math.stackexchange.com/questions/483922/blow-up-of-solutions-to-parabolic-pde as I didn't get any attention)