EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUA

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div(|▽u|p-2▽u)= |u|mu, (x,t) ∈ [0,+∞) ×Ωwith p ＞ 2 and m ＞ 0. He deals with the global solutions by D.H.Sattinger's potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded,the global nonexistence of solutions is verified by using the analysis method.

作 者： Ye Yaojun   作者單位： Department of Information and Computational Science, Henan Agricultural University, Zhengzhou 450002, China;The Graduate School of China Academy of Engineering Physics, P.O.Box 2101, Beijing 100088, China  刊 名： 數(shù)學物理學報（英文版）  ISTIC SCI 英文刊名： ACTA MATHEMATICA SCIENTIA  年，卷(期)： 2005 25(4)  分類號： O4  關鍵詞： Degenerate hyperbolic equations   global existence and global nonexistence   initial-boundary value problem  

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