Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503123 | Journal of Mathematical Analysis and Applications | 2005 | 25 Pages |
Abstract
We investigate finite-time blow-up and stability of semilinear partial differential equations of the form âwt/ât=Îwt+νtÏwt1+β, w0(x)=Ï(x)⩾0, xâR+, where Î is the generator of the standard gamma process and ν>0, ÏâR, β>0 are constants. We show that any initial value satisfying c1xâa1⩽Ï(x), x>x0, for some positive constants x0, c1, a1, yields a non-global solution if a1β<1+Ï. If Ï(x)⩽c2xâa2,x>x0, where x0,c2,a2>0, and a2β>1+Ï, then the solution wt is global and satisfies 0⩽wt(x)⩽Ctâa2,x⩾0, for some constant C>0. This complements the results previously obtained in [M. Birkner et al., Proc. Amer. Math. Soc. 130 (2002) 2431; M. Guedda, M. Kirane, Bull. Belg. Math. Soc. Simon Stevin 6 (1999) 491; S. Sugitani, Osaka J. Math. 12 (1975) 45] for symmetric α-stable generators. Systems of semilinear PDEs with gamma generators are also considered.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
José Alfredo López-Mimbela, Nicolas Privault,