no. 3
Semilinear parabolic equation in 𝐑 N associated with critical Sobolev exponent
Annales de l'I.H.P. Analyse non linéaire, Tome 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 , N⩾3, 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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     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},
     year = {2010},
     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, Tome 27 (2010) no. 3, pp. 877-900. doi: 10.1016/j.anihpc.2010.01.002

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