## Abstract

Semilinear parabolic boundary value problems with degenerated elliptic part where the right-hand side depends on the solution are studied. We approximate the parabolic semilinear problem by a system of linear degenerate elliptic problems by the aid of semidiscretization in time. Using weighted Sobolev spaces one derives a-priori-estimates for the approximate solutions. These approximate solutions converge to a uniquely determined weak solution, if the time interval is sufficiently small. We point out that the nonlinear right-hand side is defined only in a neighbourhood of the initial data, therefore one has to prove Lm-estimates for the solutions of the approximate problems.

Original language | English |
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Pages (from-to) | 5-20 |

Number of pages | 16 |

Journal | Mathematische Nachrichten |

Volume | 200 |

Publication status | Published - 1999 |

## Keywords

- semidiscretization in time
- semilinear degenerated parabolic equations
- local solutions
- ORLICZ-SOBOLEV SPACES
- SYSTEMS