Abstract
In this paper, we consider a quasi-linear parabolic equation u_t=u^p(x_{xx}+u). It is known that there exist blow-up solutions and some of them develop Type II singularity. However, only a few results are known about the precise behavior of Type II blow-up solutions for p>2. We investigated the blow-up solutions for the equation with periodic boundary conditions and derived upper estimates of the blow-up rates in the case of 2<p<3 and in the case of p=3, separately. In addition, we assert that if 2 le p le 3 then lim _{t nearrow T}(T-t)^{frac{1}{p}+varepsilon }max u(x,t)=0 z for any varepsilon >0 under some assumptions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Japan Journal of Industrial and Applied Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
