Advances in Differential Equations
- Adv. Differential Equations
- Volume 1, Number 1 (1996), 51-72.
Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces
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 () and Gurtin-Soner-Souganidis ().
Adv. Differential Equations, Volume 1, Number 1 (1996), 51-72.
First available in Project Euclid: 25 April 2013
Permanent link to this document
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. https://projecteuclid.org/euclid.ade/1366896314