Geodesic
Critical exponents of instantaneous blow-up or local solubility of non-linear equations of Sobolev type
Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 955-1012.

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We consider Cauchy problems for a class of non-linear equations of Sobolev type. It is shown that for such problems there is a critical exponent (depending on the dimension of the space $\mathbb{R}^N$) according to which a weak local solution either exists uniquely or does not exist.
Keywords: Fujita's critical exponent, non-linear equations of Sobolev type, blow-up, local solubility, non-linear capacity. 
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M. O. Korpusov. Critical exponents of instantaneous blow-up or local solubility of non-linear equations of Sobolev type. Izvestiya. Mathematics , Tome 79 (2015) no. 5, pp. 955-1012. http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a4/

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