Generalized motion of hypersurfaces whose growth speed depends superlinearly on the curvature tensor. (English) Zbl 0808.35007

Goto, Shun’ichi

Differ. Integral Equ. 7, No. 2, 323-343 (1994).

Summary: We prove a comparison principle for viscosity solution with finite speed for its level set, which solves degenerate parabolic equations with discontinuity. We also prove the (global) existence of solution in the class of viscosity solution with finite speed for the initial value problem. Our comparison and existence results yield a unique global-in- time generalized solution to interface evolution equations whose speed grows superlinearly in curvature tensors.

MSC:

35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35K15	Initial value problems for second-order parabolic equations
35K65	Degenerate parabolic equations
35K55	Nonlinear parabolic equations
35R05	PDEs with low regular coefficients and/or low regular data

Keywords:

viscosity solution with finite speed