CONSERVATION OF THE MASS FOR SOLUTIONS TO A CLASS OF SINGULAR PARABOLIC EQUATIONS


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FINO A. Z. , DÜZGÜN F. G. , Vespri V.

KODAI MATHEMATICAL JOURNAL, vol.37, no.3, pp.519-531, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.2996/kmj/1414674606
  • Title of Journal : KODAI MATHEMATICAL JOURNAL
  • Page Numbers: pp.519-531

Abstract

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 ( 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.

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.