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| TRIPLE INTERACTIONS OF CONORMAL WAVES FOR HIGHER ORDER SEMILINEAR HYPERBOLIC EQUATIONS |
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Citation： |
Fang Daoyuan.TRIPLE INTERACTIONS OF CONORMAL WAVES FOR HIGHER ORDER SEMILINEAR HYPERBOLIC EQUATIONS[J].Chinese Annals of Mathematics B,1995,16(1):23~32 |
| Page view： 1108
Net amount： 628 |
Authors： |
Fang Daoyuan; |
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| Abstract： |
The interaction of three conormal waves for semi-linear strictly hyperbolic equations of third order is considered.Let $\sigma _i,i=1,2,3$,be smooth characteristic surfaces for $P=D_t(D_t ^2- \delta)$ intersecting transversally at the origin.Suppose that the solution u to $Pu=f(t,x,y,D^ \alpha u),|\alpha|\leq 2$ is conormal to $\sigma _i,i=1,2,3$,for $t<0$.The author uses Bony's second microlocalization techniques and commutator arguments to conclude that the new singularities a short time after the triple interaction lie on the surface of the light cone $\gamma$ over the origin plus the surfaces obtained by flow-outs of the lines of intersection $\gamma \bigcap \sigma _i$ and $\sigma _i \bigcap \sigma _j,i,j=1,2,3$. |
Keywords： |
Hyperbolic equation, Conormal wave, Interaction, Characteristic surface. |
Classification： |
35L75. |
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