We consider the semilinear parabolic equation on the whole space , , where the exponent is associated with the Sobolev imbedding . First, we study the decay and blow-up of the solution by means of the potential-well and forward self-similar transformation. Then, we discuss blow-up in infinite time and classify the orbit.
Cite this article
Ryo Ikehata, Michinori Ishiwata, Takashi Suzuki, Semilinear parabolic equation in associated with critical Sobolev exponent. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 3, pp. 877–900DOI 10.1016/J.ANIHPC.2010.01.002