2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.
The problem studied here was suggested to us by V. Petkov.
Since the beginning of our careers, we have benefitted from his insights in
partial differential equations and mathematical physics. In his writings and
many discussions, the conjuction of deep analysis and specially interesting
problems has been a source inspiration for us.
The research of J. Rauch is partially supported by the U.S. National Science Foundation
under...
In this paper we study the Cauchy problem for second order strictly hyperbolic operators of the form
when the coefficients of the principal part are not Lipschitz continuous, but only “Log-Lipschitz” with respect to all the variables. This class of equation is invariant under changes of variables and therefore suitable for a local analysis. In particular, we show local existence, local uniqueness and finite speed of propagation for the noncharacteristic Cauchy problem. This provides an invariant...
We prove that the Cauchy problem for a class of hyperbolic equations with non-Lipschitz coefficients is well-posed in and in Gevrey spaces. Some counter examples are given showing the sharpness of these results.
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