Global solutions of the exponential wave equation with small initial data
Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 811-821
Printed May 31, 2013
Hyungjin Huh
Chung-Ang University
Abstract : We study the initial value problem of the exponential wave equation in $\mathbb{R }^{n+1}$ 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 $\phi=0$.
Keywords : quasilinear wave, weakly linearly degenerate, double null form
MSC numbers : 35L60, 35L70
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