Kodai Mathematical Journal

Conservation of the mass for solutions to a class of singular parabolic equations

Ahmad Z. Fino, Fatma Gamze Düzgün, and Vincenzo Vespri

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In this paper we deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L coefficients, whose prototypes are the p-Laplacian $\frac{2N}{N+1}<p<2$ and the Porous medium equation $((\frac{N-2}{N})_+<m<1)$. In this range of the parameters p and m, we are in the so called fast diffusion case. We prove that the initial mass is preserved for all the times.

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Kodai Math. J., Volume 37, Number 3 (2014), 519-531.

First available in Project Euclid: 30 October 2014

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Fino, Ahmad Z.; Düzgün, Fatma Gamze; Vespri, Vincenzo. Conservation of the mass for solutions to a class of singular parabolic equations. Kodai Math. J. 37 (2014), no. 3, 519--531. doi:10.2996/kmj/1414674606. https://projecteuclid.org/euclid.kmj/1414674606

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