The Fujita phenomenon in exterior domains under the Robin boundary conditions
نویسندگان
چکیده
The Fujita phenomenon for nonlinear parabolic problems ∂tu = ∆u+ u p in an exterior domain of R under the Robin boundary conditions is investigated in the superlinear case. As in the case of Dirichlet boundary conditions (see Trans. Amer. Math. Soc 316 (1989), 595-622 and Isr. J. Math. 98 (1997), 141-156), it turns out that there exists a critical exponent p = 1+2/N such that blow-up of positive solutions always occurs for subcritical exponents, whereas in the supercritical case global existence can occur for small non-negative initial data.
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