Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I am reading an articule(http://link.springer.com/content/pdf/10.1007%2Fs00028-010-0085-8.pdf) so I almost done but I dont understand the next argument is in the page 8 "It is known from the classical parabolic theory that in the case when the nonlinearity grows no faster than quadratically in the gradient, it is sufficient to prove $L^{\infty}$- apriori estimate to guarantee global in time existence for the solutions" the questions are: 1) whats means the nonlinearity grows no faster than quadratically in the gradient ? 2) why the below argument guarantee global solutions?

note: i cant get the references... :(

Thank for your answers !

share|improve this question
add comment

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.