Weakly hyperbolic equations with non-analytic coefficients and lower order terms

@article{Garetto2013WeaklyHE,
  title={Weakly hyperbolic equations with non-analytic coefficients and lower order terms},
  author={Claudia Garetto and M. Ruzhansky},
  journal={Mathematische Annalen},
  year={2013},
  volume={357},
  pages={401-440}
}
  • Claudia Garetto, M. Ruzhansky
  • Published 2013
  • Mathematics
  • Mathematische Annalen
  • In this paper we consider weakly hyperbolic equations of higher orders in arbitrary dimensions with time-dependent coefficients and lower order terms. We prove the Gevrey well-posedness of the Cauchy problem under $$C^k$$-regularity of coefficients of the principal part and natural Levi conditions on lower order terms which may be only continuous. In the case of analytic coefficients in the principal part we establish the $$C^\infty $$ well-posedness. The proofs are based on using the quasi… CONTINUE READING
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    References

    SHOWING 1-10 OF 23 REFERENCES
    Asymptotic integration and dispersion for hyperbolic equations
    • 16
    • PDF
    Homogeneous weakly hyperbolic equations with time dependent analytic coefficients
    • 11
    • Highly Influential
    On the well-posedness of weakly hyperbolic equations with time dependent coefficients
    • 19
    • PDF
    Dispersive and Strichartz Estimates for Hyperbolic Equations With Constant Coefficients
    • 30
    • PDF
    Hyperbolic Equations with Non-analytic Coefficients
    • 28
    • Highly Influential
    Non-uniqueness in hyperbolic Cauchy problems
    • 38
    • Highly Influential