Title | QUENCHING FOR DEGENERATE PARABOLIC PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS |

Publication Type | Journal Article |

Year of Publication | 2009 |

Authors | CHAN C.Y, LIU H.T |

Journal | Dynamic Systems and Applications |

Volume | 18 |

Start Page | 17 |

Pagination | 12 |

Date Published | 2009 |

ISSN | 1056-2176 |

AMS Subject Classification | 35K20, 35K55, 35K57, 35K60, 35K65 |

Abstract | Let q be a nonnegative real number, and a and T be positive constants. This article studies the following degenerate parabolic problem: x qut − uxx = G(u) in (0, a) × (0, T], where G is a nonnegative function in the form of either f(u(x, t)), or Ra 0 h(x, t) f(u(x, t))dx for some positive, bounded and continuous function h with f > 0, f 0> 0, f 00≥ 0, and limu→1− f(u) = ∞. It is subject to the initial condition, u(x, 0) = 0 on [0, a], and the boundary conditions, u(0, t) = Za 0 M(x)|u (x, t)| p dx, u (a, t) = Za 0 N (x)|u (x, t)| r dx, t > 0, where p and r are constants greater than or equal to 1, and M and N are given nonnegative functions. Existence, uniqueness and criteria for quenching and non-quenching are studied. |

https://acadsol.eu/dsa/articles/18/02-DSA-CY-2-ChanLiu.pdf | |

Refereed Designation | Refereed |