The Fundamental Solution for a Second Order Weakly Hyperbolic Cauchy problem
We construct the fundamental solution for a weakly hyperbolic operator satisfying an intermediate condition between effective hyperbolicity and the Levi condition. By the fundamental solution, we obtain the well-posedness in C⋅ of the Cauchy problem.
KeywordsWeakly Hyperbolic Equations Cauchy Problem
Mathematics Subject Classification (2000)35L80 35L15
- H. Kumano-Go, Pseudo-differential operators, The MIT Press, Cambridge, Massachusetts, and London, England, 1981.Google Scholar