Semilinear parabolic equation in 𝐑 N associated with critical Sobolev exponent
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 3, pp. 877-900.

We consider the semilinear parabolic equation u t -Δu=|u| p-1 u on the whole space 𝐑 N , N3, where the exponent p=(N+2)/(N-2) is associated with the Sobolev imbedding H 1 (𝐑 N )L p+1 (𝐑 N ). 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.

DOI: 10.1016/j.anihpc.2010.01.002
Classification: 35K55
Keywords: Parabolic equation, Critical Sobolev exponent, Cauchy problem, Stable and unstable sets, Self-similarity
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     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},
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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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