TY - JOUR
T1 - On the dynamics of a strongly singular parabolic equation
AU - Trachanas, Georgios P.
AU - Zographopoulos, Nikolaos B.
N1 - Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - In this paper we study the semiflow defined by a semilinear parabolic equation, in which both the diffusion and the reaction term present strong order of singularity at the origin. We justify the existence of a global branch of nontrivial equilibrium solutions for subcritical nonlinearities. The approach, based on the critical Caffarelli-Kohn-Nirenberg inequality, follows the arguments of [21,22].
AB - In this paper we study the semiflow defined by a semilinear parabolic equation, in which both the diffusion and the reaction term present strong order of singularity at the origin. We justify the existence of a global branch of nontrivial equilibrium solutions for subcritical nonlinearities. The approach, based on the critical Caffarelli-Kohn-Nirenberg inequality, follows the arguments of [21,22].
KW - Global attractor
KW - Global bifurcation
KW - Singularities
UR - http://www.scopus.com/inward/record.url?scp=84940365092&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2014.06.071
DO - 10.1016/j.jmaa.2014.06.071
M3 - Article
AN - SCOPUS:84940365092
SN - 0022-247X
VL - 421
SP - 21
EP - 37
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -