TY - JOUR
T1 - Nonlinear Diffusion Equations on Unbounded Fractal Domains
AU - Falconer, Kenneth John
AU - Hu, J
PY - 2001/4/15
Y1 - 2001/4/15
N2 - We investigate the nonlinear diffusion equation partial derivativeu/partial derivativet Deltau + up, p > 1, on certain unbounded fractal domains, where Delta is the infinitesimal generator of the semigroup associated with a corresponding heat kernel. We show that there are nonnegative global solutions for non-negative initial data if p > If 2/d(s), while solutions blow up if p less than or equal to 1 + 2/d(s), where d(s) is the spectral dimension of the domain. We investigate smoothness and Holder continuity of solutions when they exist. (C) 2001 Academic Press.
AB - We investigate the nonlinear diffusion equation partial derivativeu/partial derivativet Deltau + up, p > 1, on certain unbounded fractal domains, where Delta is the infinitesimal generator of the semigroup associated with a corresponding heat kernel. We show that there are nonnegative global solutions for non-negative initial data if p > If 2/d(s), while solutions blow up if p less than or equal to 1 + 2/d(s), where d(s) is the spectral dimension of the domain. We investigate smoothness and Holder continuity of solutions when they exist. (C) 2001 Academic Press.
KW - BROWNIAN-MOTION
UR - http://www.scopus.com/inward/record.url?scp=0035872058&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1006/jmaa.2000.7331
U2 - 10.1006/jmaa.2000.7331
DO - 10.1006/jmaa.2000.7331
M3 - Article
SN - 0022-247X
VL - 256
SP - 606
EP - 624
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -