Advances in Differential Equations

Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces

Hitoshi Ishii

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We establish comparison theorems for solutions of degenerate parabolic partial differential equations with discontinuities (or singularities). The results are used to define the generalized evolutions of sets generated by geometric partial differential equations with discontinuities. These results generalize recent results obtained by Ohnuma-Sato ([13]) and Gurtin-Soner-Souganidis ([11]).

Article information

Adv. Differential Equations, Volume 1, Number 1 (1996), 51-72.

First available in Project Euclid: 25 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K65: Degenerate parabolic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]


Ishii, Hitoshi. Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces. Adv. Differential Equations 1 (1996), no. 1, 51--72.

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