Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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GLOBAL SOLUTIONS OF THE EXPONENTIAL WAVE EQUATION WITH SMALL INITIAL DATA

  • Received : 2012.03.06
  • Published : 2013.05.31
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Abstract

We study the initial value problem of the exponential wave equation in $\math{R}^{n+1}$ for small initial data. We shows, in the case of $n=1$, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When $n{\geq}2$, a vector field method is applied to show the stability of a trivial solution ${\phi}=0$.

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Acknowledgement

Supported by : Chung-Ang University

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