Positive solution to semilinear parabolic equation associated with critical Sobolev exponent |
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| Authors: | Michinori Ishiwata Takashi Suzuki |
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| Institution: | 1. Department of Industrial System, Faculty of Symbiotic Systems Science, Fukushima University, Fukushima, 960-1296, Japan
2. Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonakashi, 560-8531, Japan
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| Abstract: | We study the semilinear parabolic equation ${u_{t}- \Delta u = u^{p}, u \geq 0}$ on the whole space R N , ${N \geq 3}$ associated with the critical Sobolev exponent p = (N + 2)/(N ? 2). Similarly to the bounded domain case, there is threshold blowup modulus concerning the blowup in finite time. Furthermore, global in time behavior of the threshold solution is prescribed in connection with the energy level, blowup rate, and symmetry. |
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