Well-posedness results and blow-up for a semi-linear time fractional diffusion equation with variable coefficients
Keyword(s):
Blow Up
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<p style='text-indent:20px;'>The semi-linear problem of a fractional diffusion equation with the Caputo-like counterpart of a hyper-Bessel differential is considered. The results on existence, uniqueness and regularity estimates (local well-posedness) of the solutions are established in the case of linear source and the source functions that satisfy the globally Lipschitz conditions. Moreover, we prove that the problem exists a unique positive solution. In addition, the unique continuation of solutions and a finite-time blow-up are proposed with the reaction terms are logarithmic functions.</p>
2013 ◽
Vol 21
(9)
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pp. 1769-1777
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2020 ◽
Vol 375
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pp. 112811
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2017 ◽
Vol 18
(5)
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pp. 385-393
2021 ◽
Vol 0
(0)
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2017 ◽
Vol 73
(6)
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pp. 1155-1171
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