Advances in Differential Equations

Generalized solutions of degenerate second-order quasilinear parabolic and elliptic equations

A. I. Volpert

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Abstract

Generalized (entropy) solutions of degenerate second-order quasilinear parabolic and elliptic equations are considered. In classes of functions under consideration it is proved that a function is a generalized solution if and only if it is a weak solution and satisfies discontinuity conditions. Uniqueness and stability of the generalized solution of the Cauchy problem for a degenerate parabolic equation is proved.

Article information

Source
Adv. Differential Equations Volume 5, Number 10-12 (2000), 1493-1518.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651231

Mathematical Reviews number (MathSciNet)
MR1785683

Zentralblatt MATH identifier
0988.35091

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B35: Stability 35J70: Degenerate elliptic equations 35K65: Degenerate parabolic equations 35L67: Shocks and singularities [See also 58Kxx, 76L05]

Citation

Volpert, A. I. Generalized solutions of degenerate second-order quasilinear parabolic and elliptic equations. Adv. Differential Equations 5 (2000), no. 10-12, 1493--1518. https://projecteuclid.org/euclid.ade/1356651231.


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