### Abstract

We consider a quasilinear parabolic boundary value problem, the elliptic part of which degenerates near the boundary. In order to solve this problem, we approximate it by a system of linear degenerate elliptic boundary value problems by means of semidiscretization with respect to time. We use the theory of degenerate elliptic operators and weighted Sobolev spaces to find a priori estimates for the solutions of the approximating problems. These solutions converge to a local solution, if the step size of the time-discretization goes to zero. It is worth pointing out that we do not require any growth conditions on the nonlinear coefficients and right-hand side, since we are able to prove L-infinity-estimates.

Original language | English |
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Pages (from-to) | 109-129 |

Number of pages | 21 |

Journal | Mathematische Nachrichten |

Volume | 198 |

Publication status | Published - 1999 |

### Keywords

- semidiscretization in time
- quasilinear degenerate parabolic equations
- local solutions
- ORLICZ-SOBOLEV SPACES
- SYSTEMS

## Cite this

*Mathematische Nachrichten*,

*198*, 109-129.