| Lu QIkENG,Yin Weiping.[J].数学年刊A辑,1980,1(1):115~129 |
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| THE SOLUTION OF THE CAUCHY PROBLEM FOR A WAVEEQUATION WITH VARIABLE COEFFICIENTS |
| Received:August 30, 1978 |
| DOI： |
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| 英文摘要: |
| Let \[{\mathfrak{M}_k}\] denote the space of Lorentz witb. constant curvature:
\[1 + {K_{\eta pq}}{x^p}{x^q}\]
where K is a constant and \[\eta = ({\eta _{pq}})\]=diag [1,... 1,-1], We have considered the
wave equation with variable coefficients
\[\frac{\partial }{{\partial {x^j}}}(\sqrt {|\tilde g|} ){{\tilde g}^{jk}}\frac{{\partial u}}{{\partial {x^k}}}) = 0\]
in \[{\mathfrak{M}_k}\] where
\[|\tilde g| = |1 + {K_{\eta pq}}{x^p}{x^q}{|^{ - (n + 1)}},{{\tilde g}^{jk}} = (1 + {K_{\eta pq}}{x^p}{x^q})({\eta _{jk}} + K{x^j}{x^k})\]
and found the explicit solution of the Cauchy problem for equation (1) |
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