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On the Cauchy problem for hyperbolic functional-differential equations

Volume 115 / 2015

Adrian Karpowicz, Henryk Leszczyński Annales Polonici Mathematici 115 (2015), 53-74 MSC: Primary 35A01; Secondary 35L71, 35R10. DOI: 10.4064/ap115-1-5

Abstract

We consider the Cauchy problem for a nonlocal wave equation in one dimension. We study the existence of solutions by means of bicharacteristics. The existence and uniqueness is obtained in $W^{1,\infty }_{\rm loc}$ topology. The existence theorem is proved in a subset generated by certain continuity conditions for the derivatives.

Authors

  • Adrian KarpowiczInstitute of Mathematics
    University of Gdańsk
    80-952 Gdańsk, Poland
    e-mail
  • Henryk LeszczyńskiInstitute of Mathematics
    University of Gdańsk
    80-952 Gdańsk, Poland
    e-mail

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