LOCAL AND MICROLOCAL CAUCHY PROBLEM FOR NON-EFFECTIVELY HYPERBOLIC OPERATORS

作者：Nishitani Tatsuo^*

来源：Journal of Hyperbolic Differential Equations, 2014, 11(1): 185-213.

DOI：10.1142/S0219891614500052

• Microlocal Cauchy problem
• well-posedness
• finite propagation speed
• non-effectively hyperbolic operator
• spatial type

We study differential operators of order 2 and establish new energy estimates which ensure that the micro supports of solutions to the Cauchy problem propagate with finite speed. We then study the Cauchy problem for non-effectively hyperbolic operators with no null bicharacteristic tangent to the doubly characteristic set and with zero positive trace. By checking the energy estimates, we ensure the propagation with finite speed of the micro supports of solutions, and we prove that the Cauchy problem for such non-effectively hyperbolic operators is C-infinity well-posed if and only if the Levi condition holds.

• 出版日期2014-3