In this paper we deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L-infinity coefficients, whose prototypes are the p-Laplacian (2N/N+1 < p < 2) and the Porous medium equation ((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.
Conservation of the mass for solutions to a class of singular parabolic equations
Duzgun, Fatma Gamze;Vespri, Vincenzo
2014-01-01
Abstract
In this paper we deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L-infinity coefficients, whose prototypes are the p-Laplacian (2N/N+1 < p < 2) and the Porous medium equation ((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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