Local decay of solutions of conservative first order hyperbolic systems in odd dimensional space

Author:
James V. Ralston

Journal:
Trans. Amer. Math. Soc. **194** (1974), 27-51

MSC:
Primary 35L45

DOI:
https://doi.org/10.1090/S0002-9947-1974-0352714-9

MathSciNet review:
0352714

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Abstract: This paper deals with symmetric hyperbolic systems, , where *L* is equal to the homogeneous, constant coefficient operator for . Under the hypothesis that *L* has simple null bicharacteristics and these propagate to infinity, local decay of solutions and completeness of the wave operators relating solutions of and solutions of are established. Results of this type for elliptic *L* are due to Lax and Phillips. The proof here is based, in part, on a new estimate of the regularity of the -solutions of the equation for smooth *g* with support in .

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DOI:
https://doi.org/10.1090/S0002-9947-1974-0352714-9

Article copyright:
© Copyright 1974
American Mathematical Society