### Abstract

The comparison, uniqueness and existence of viscosity solutions to the Cauchy-Dirichlet problem are proved for a degenerate parabolic equation of the form u_{t} = Δ_{∞}u, where Δ_{∞} denotes the so-called infinity-Laplacian given by Δ_{∞}u = Σ^{N}_{i,j=1} u_{xi}u_{xj} u _{xixj}. Our proof relies on a coercive regularization of the equation, barrier function arguments and the stability of viscosity solutions.

Original language | English |
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Pages (from-to) | 18-27 |

Number of pages | 10 |

Journal | Discrete and Continuous Dynamical Systems- Series A |

Issue number | SUPPL. |

Publication status | Published - 2007 Sep 1 |

Externally published | Yes |

### Keywords

- Degenerate parabolic equation
- Infinity-Laplacian
- Viscosity solution

### ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Akagi, G., & Suzuki, K. (2007). On a certain degenerate parabolic equation associated with the infinity-Laplacian.

*Discrete and Continuous Dynamical Systems- Series A*, (SUPPL.), 18-27.