Instantaneous and finite time blow-up of solutions toareaction-diffusion equation with Hardy-type singular potential
Fecha
2020
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Elsevier
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Resumen
We deal with radially symmetric solutions to the reaction-diffusion equation with
Hardy-type singular potential
ut = Δum +
K
|x|2 um,
posed in RN × (0, T), in dimension N ≥ 3, where m > 1 and 0 <K< (N − 2)2/4.
We prove that, in dependence of the initial condition u0 ∈ L∞(RN ) ∩ C(RN ),
its solutions may either blow up instantaneously or blow up in finite time at the
origin, thus developing a singularity at x = 0, but they can be continued globally
in weak sense. The instantaneous blow-up occurs for example for any data u0 such
that u0(0) > 0. The proofs are based on a transformation mapping solutions to our
equation into solutions to a non-homogeneous porous medium equation.
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Citación
Razvan Gabriel Iagar, Ariel Sánchez, Instantaneous and finite time blow-up of solutions to a reaction-diffusion equation with Hardy-type singular potential, Journal of Mathematical Analysis and Applications, Volume 491, Issue 1, 2020, 124244, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2020.124244
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