Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900805 | Applied Mathematics and Computation | 2018 | 13 Pages |
Abstract
This paper deals with the dead-core rate for the fast diffusion equation with a strong absorption in several space dimensions
ut=Îumâup,(x,t)âΩÃ(0,â),where 0â¯<â¯pâ¯<â¯mâ¯<â¯1 and Ω=B(0,1)={xâRN:|x|<1} with Nâ¯â¥â¯1. By using the self-similar transformation technique and the Zelenyak method, in higher dimensional radially symmetric cases, we prove that the dead-core rate is not self-similar. Moreover, we also give the precise estimates on the single-point final dead-core profile. Finally, when the absorption term âup is replaced by âa(x,t)up, then we derive that the dead-core rate can turn into the corresponding ODE rate if the coefficient function a(x, t) is a suitable uniformly bounded positive function, which implies that a(x, t) plays an important role in the study of the dead-core rate. The main aim of this paper is to extend the results obtained by Guo et al. (2010) to the higher dimensional radially symmetric case.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Pan Zheng, Chunlai Mu, Xuegang Hu,