Acta mathematica scientia,Series B

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

Ye Yaojun   

  • Online:2005-10-11 Published:2005-10-11
  • Supported by:

    Project supported by NSF of China (10441002) and Henan
    Province(0111051200) and Henan Province Education Department(200510466011)

Abstract:

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,+∞) ×

with 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.

Key words: Degenerate hyperbolic equations, global existence and global nonexistence,
initial-boundary value problem

CLC Number: 

  • 35L10
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