Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591487 | Journal of Functional Analysis | 2010 | 26 Pages |
Abstract
We deal with the following parabolic problem,{utâÎu+|âu|p=λu|x|2+f,u>0inΩÃ(0,T),u(x,t)=0onâΩÃ(0,T),u(x,0)=u0(x),xâΩ, where ΩâRN, N⩾3, is a bounded regular domain such that 0âΩ or Ω=RN, 1
0 and f⩾0, u0⩾0 are in a suitable class of functions. For p>pââ¡NNâ1, we will show that the above problem has a solution for all λ>0, fâL1(ΩT) and u0âL1(Ω). We prove also that pâ is optimal for the existence result. These results prove the strong regularizing effect of a gradient term in the problem studied in Baras and Goldstein (1984) [3]. The Cauchy problem is also studied.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Boumediene Abdellaoui, Ireneo Peral, Ana Primo,