Semilinear parabolic equation in $ {\mathbf{R}}^{N}$ associated with critical Sobolev exponent

Ikehata, Ryo; Ishiwata, Michinori; Suzuki, Takashi

Semilinear parabolic equation in

𝐑^{N}

associated with critical Sobolev exponent

Ikehata, Ryo ; Ishiwata, Michinori ; Suzuki, Takashi

Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010), p. 877-900 / Harvested from Numdam

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Résumé

We consider the semilinear parabolic equation $u_{t} - Δ u = {| u |}^{p - 1} u$ on the whole space $𝐑^{N}$ , $N ⩾ 3$ , where the exponent $p = (N + 2) / (N - 2)$ is associated with the Sobolev imbedding $H^{1} (𝐑^{N}) \subset L^{p + 1} (𝐑^{N})$ . 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.

Publié le : 2010-01-01

MR 2629884 | Zbl 1192.35099

DOI : https://doi.org/10.1016/j.anihpc.2010.01.002
Classification: 35K55

@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},
     volume = {27},
     year = {2010},
     pages = {877-900},
     doi = {10.1016/j.anihpc.2010.01.002},
     mrnumber = {2629884},
     zbl = {1192.35099},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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, Tome 27 (2010) pp. 877-900. doi : 10.1016/j.anihpc.2010.01.002. http://gdmltest.u-ga.fr/item/AIHPC_2010__27_3_877_0/

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