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.
Keywords: Parabolic equation, Critical Sobolev exponent, Cauchy problem, Stable and unstable sets, Self-similarity
@article{AIHPC_2010__27_3_877_0, author = {Ikehata, Ryo and Ishiwata, Michinori and Suzuki, Takashi}, title = {Semilinear parabolic equation in $ {\mathbf{R}}^{N}$ associated with critical {Sobolev} exponent}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {877--900}, publisher = {Elsevier}, volume = {27}, number = {3}, year = {2010}, doi = {10.1016/j.anihpc.2010.01.002}, mrnumber = {2629884}, zbl = {1192.35099}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.002/} }
TY - JOUR AU - Ikehata, Ryo AU - Ishiwata, Michinori AU - Suzuki, Takashi TI - Semilinear parabolic equation in $ {\mathbf{R}}^{N}$ associated with critical Sobolev exponent JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 877 EP - 900 VL - 27 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.002/ DO - 10.1016/j.anihpc.2010.01.002 LA - en ID - AIHPC_2010__27_3_877_0 ER -
%0 Journal Article %A Ikehata, Ryo %A Ishiwata, Michinori %A Suzuki, Takashi %T Semilinear parabolic equation in $ {\mathbf{R}}^{N}$ associated with critical Sobolev exponent %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 877-900 %V 27 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.002/ %R 10.1016/j.anihpc.2010.01.002 %G en %F AIHPC_2010__27_3_877_0
Ikehata, Ryo; Ishiwata, Michinori; Suzuki, Takashi. Semilinear parabolic equation in $ {\mathbf{R}}^{N}$ associated with critical Sobolev exponent. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 3, pp. 877-900. doi : 10.1016/j.anihpc.2010.01.002. http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.002/
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