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

Ahmad Z. Fino; Fatma Gamze Düzgün; Vincenzo Vespri

doi:10.2996/kmj/1414674606

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

Ahmad Z. Fino
, Fatma Gamze Düzgün
, Vincenzo Vespri

Division of Analysis and Theory of Functions

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper we deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L^∞ cofficients, whose prototypes are the p-Laplacian (Formula presented.) and the Porous medium equation (Formula presented.). In this range of the parameters p and m, we are in the so called fast di¤usion case. We prove that the initial mass is preserved for all the times.

Original language	English
Pages (from-to)	519-531
Number of pages	13
Journal	Kodai Mathematical Journal
Volume	37
Issue number	3
DOIs	https://doi.org/10.2996/kmj/1414674606
Publication status	Published - 2014

Keywords

Cauchy problem
Conservation of the L norm
Singular parabolic equations

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10.2996/kmj/1414674606

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abstract = "In this paper we deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L∞ cofficients, whose prototypes are the p-Laplacian (Formula presented.) and the Porous medium equation (Formula presented.). In this range of the parameters p and m, we are in the so called fast di¤usion case. We prove that the initial mass is preserved for all the times.",

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AU - Fino, Ahmad Z.

AU - Düzgün, Fatma Gamze

AU - Vespri, Vincenzo

PY - 2014

Y1 - 2014

N2 - In this paper we deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L∞ cofficients, whose prototypes are the p-Laplacian (Formula presented.) and the Porous medium equation (Formula presented.). In this range of the parameters p and m, we are in the so called fast di¤usion case. We prove that the initial mass is preserved for all the times.

AB - In this paper we deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L∞ cofficients, whose prototypes are the p-Laplacian (Formula presented.) and the Porous medium equation (Formula presented.). In this range of the parameters p and m, we are in the so called fast di¤usion case. We prove that the initial mass is preserved for all the times.

KW - Cauchy problem

KW - Conservation of the L norm

KW - Singular parabolic equations

UR - https://www.scopus.com/pages/publications/84908509880

U2 - 10.2996/kmj/1414674606

DO - 10.2996/kmj/1414674606

M3 - Article

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SP - 519

EP - 531

JO - Kodai Mathematical Journal

JF - Kodai Mathematical Journal

IS - 3

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

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Keywords

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